Social evolution of shared biofilm matrix components.

Biofilm formation is an important and ubiquitous mode of growth among bacteria. Central to the evolutionary advantage of biofilm formation is cell-cell and cell-surface adhesion achieved by a variety of factors, some of which are diffusible compounds that may operate as classical public goods-factors that are costly to produce but may benefit other cells. An outstanding question is how diffusible matrix production, in general, can be stable over evolutionary timescales. In this work, using Vibrio cholerae as a model, we show that shared diffusible biofilm matrix proteins are indeed susceptible to cheater exploitation and that the evolutionary stability of producing these matrix components fundamentally depends on biofilm spatial structure, intrinsic sharing mechanisms of these components, and flow conditions in the environment. We further show that exploitation of diffusible adhesion proteins is localized within a well-defined spatial range around cell clusters that produce them. Based on this exploitation range and the spatial distribution of cell clusters, we constructed a model of costly diffusible matrix production and related these length scales to the relatedness coefficient in social evolution theory. Our results show that production of diffusible biofilm matrix components is evolutionarily stable under conditions consistent with natural biofilm habitats and host environments. We expect the mechanisms revealed in this study to be relevant to other secreted factors that operate as cooperative public goods in bacterial communities and the concept of exploitation range and the associated analysis tools to be generally applicable.

New Insights into Vibrio cholerae Biofilms from Molecular Biophysics to Microbial Ecology.

With the discovery that 48% of cholera infections in rural Bangladesh villages could be prevented by simple filtration of unpurified waters and the detection of Vibrio cholerae aggregates in stools from cholera patients it was realized V. cholerae biofilms had a central function in cholera pathogenesis. We are currently in the seventh cholera pandemic, caused by O1 serotypes of the El Tor biotypes strains, which initiated in 1961. It is estimated that V. cholerae annually causes millions of infections and over 100,000 deaths. Given the continued emergence of cholera in areas that lack access to clean water, such as Haiti after the 2010 earthquake or the ongoing Yemen civil war, increasing our understanding of cholera disease remains a worldwide public health priority. The surveillance and treatment of cholera is also affected as the world is impacted by the COVID-19 pandemic, raising significant concerns in Africa. In addition to the importance of biofilm formation in its life cycle, V. cholerae has become a key model system for understanding bacterial signal transduction networks that regulate biofilm formation and discovering fundamental principles about bacterial surface attachment and biofilm maturation. This chapter will highlight recent insights into V. cholerae biofilms including their structure, ecological role in environmental survival and infection, regulatory systems that control them, and biomechanical insights into the nature of V. cholerae biofilms.

Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals.

Liquid crystals are widely known for their facile responses to external fields, which forms a basis of the modern information display technology. However, switching of molecular alignment field configurations typically involves topologically trivial structures, although singular line and point defects often appear as short-lived transient states. Here, we demonstrate electric and magnetic switching of nonsingular solitonic structures in chiral nematic and ferromagnetic liquid crystals. These topological soliton structures are characterized by Hopf indices, integers corresponding to the numbers of times that closed-loop-like spatial regions (dubbed "preimages") of two different single orientations of rod-like molecules or magnetization are linked with each other. We show that both dielectric and ferromagnetic response of the studied material systems allow for stabilizing a host of topological solitons with different Hopf indices. The field transformations during such switching are continuous when Hopf indices remain unchanged, even when involving transformations of preimages, but discontinuous otherwise.

Hopf Solitons in Helical and Conical Backgrounds of Chiral Magnetic Solids.

Three-dimensional topological solitons attract a great deal of interest in fields ranging from particle physics to cosmology, but remain experimentally elusive in solid-state magnets. Here we numerically predict magnetic heliknotons, an embodiment of such nonzero-Hopf-index solitons localized in all spatial dimensions while embedded in a helical or conical background of chiral magnets. We describe conditions under which heliknotons emerge as metastable or ground-state localized nonsingular structures with fascinating knots of magnetization field in widely studied materials. We demonstrate magnetic control of three-dimensional spatial positions of such solitons, as well as show how they interact to form moleculelike clusters and possibly even crystalline phases comprising three-dimensional lattices of such solitons with both orientational and positional order. Finally, we discuss both fundamental importance and potential technological utility of magnetic heliknotons.

Super-resolution stimulated emission depletion microscopy of director structures in liquid crystals: publisher's note.

This publisher's note corrects errors in the body text of Opt. Lett.43, 5158 (2018)OPLEDP0146-959210.1364/OL.43.005158.

Super-resolution stimulated emission depletion microscopy of director structures in liquid crystals.

Extending the optical imaging of director structures in liquid crystals (LCs) beyond the diffraction limit is poised to provide insights into previously elusive LC physics at the nanoscale. Here, we develop and characterize super-resolution stimulated emission depletion microscopy with molecular orientation sensitivity and apply it to reveal spatially localized director structures in chiral nematic and smectic LCs. As examples, we demonstrate director imaging and reconstruction of nanoscale LC configurations, including solitonic Bloch walls and two-dimensional skyrmions, both observed in sub-micrometer-thick strongly confined LC films, and focal conic domains in smectic LCs. The ≲100 nm resolution of our orientation-resolved STED imaging is three times better than that of fluorescence confocal polarizing microscopy and polarized nonlinear imaging techniques, but can be potentially improved even further.

Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures.

Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have not been demonstrated as stable spatially localized structures in solid-state magnetic materials. Here we model the existence of such static solitons with different Hopf index values in noncentrosymmetric solid magnetic nanostructures with a perpendicular interfacial magnetic anisotropy. We show how this surface anisotropy, along with the Dzyaloshinskii-Moriya interactions and the geometry of nanostructures, stabilize hopfions. We demonstrate knots in emergent field lines and computer simulate Lorentz transmission electron microscopy images of such solitonic configurations to guide their experimental discovery in magnetic solids.

Field-controlled dynamics of skyrmions and monopoles.

Magnetic monopoles, despite their ongoing experimental search as elementary particles, have inspired the discovery of analogous excitations in condensed matter systems. In chiral condensed matter systems, emergent monopoles are responsible for the onset of transitions between topologically distinct states and phases, such as in the case of transitions from helical and conical phase to A-phase comprising periodic arrays of skyrmions. By combining numerical modeling and optical characterizations, we describe how different geometrical configurations of skyrmions terminating at monopoles can be realized in liquid crystals and liquid crystal ferromagnets. We demonstrate how these complex structures can be effectively manipulated by external magnetic and electric fields. Furthermore, we discuss how our findings may hint at similar dynamics in other physical systems and their potential applications.

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.

Geometric transformation and three-dimensional hopping of Hopf solitons.

Arising in many branches of physics, Hopf solitons are three-dimensional particle-like field distortions with nontrivial topology described by the Hopf map. Despite their recent discovery in colloids and liquid crystals, the requirement of applied fields or confinement for stability impedes their utility in technological applications. Here we demonstrate stable Hopf solitons in a liquid crystal material without these requirements as a result of enhanced stability by tuning anisotropy of parameters that describe energetic costs of different gradient components in the molecular alignment field. Nevertheless, electric fields allow for inter-transformation of Hopf solitons between different geometric embodiments, as well as for their three-dimensional hopping-like dynamics in response to electric pulses. Numerical modelling reproduces both the equilibrium structure and topology-preserving out-of-equilibrium evolution of the soliton during switching and motions. Our findings may enable myriads of solitonic condensed matter phases and active matter systems, as well as their technological applications.

Nematic Order, Plasmonic Switching and Self-Patterning of Colloidal Gold Bipyramids.

Dispersing inorganic colloidal nanoparticles within nematic liquid crystals provides a versatile platform both for forming new soft matter phases and for predefining physical behavior through mesoscale molecular-colloidal self-organization. However, owing to formation of particle-induced singular defects and complex elasticity-mediated interactions, this approach has been implemented mainly just for colloidal nanorods and nanoplatelets, limiting its potential technological utility. Here, orientationally ordered nematic colloidal dispersions are reported of pentagonal gold bipyramids that exhibit narrow but controlled polarization-dependent surface plasmon resonance spectra and facile electric switching. Bipyramids tend to orient with their C5 rotation symmetry axes along the nematic director, exhibiting spatially homogeneous density within aligned samples. Topological solitons, like heliknotons, allow for spatial reorganization of these nanoparticles according to elastic free energy density within their micrometer-scale structures. With the nanoparticle orientations slaved to the nematic director and being switched by low voltages ≈1 V within a fraction of a second, these plasmonic composite materials are of interest for technological uses like color filters and plasmonic polarizers, as well as may lead to the development of unusual nematic phases, like pentatic liquid crystals.

Surface anchoring as a control parameter for stabilizing torons, skyrmions, twisted walls, fingers, and their hybrids in chiral nematics.

Chiral condensed matter systems, such as liquid crystals and magnets, exhibit a host of spatially localized topological structures that emerge from the medium's tendency to twist and its competition with confinement and field coupling effects. We show that the strength of perpendicular surface boundary conditions can be used to control the structure and topology of solitonic and other localized field configurations. By combining numerical modeling and three-dimensional imaging of the director field, we reveal structural stability diagrams and intertransformation of twisted walls and fingers, torons, and skyrmions and their crystalline organizations upon changing boundary conditions. Our findings provide a recipe for controllably realizing skyrmions, torons, and hybrid solitonic structures possessing features of both of them, which will aid in fundamental explorations and technological uses of such topological solitons. Moreover, we discuss how other material parameters can be used to determine soliton stability and how similar principles can be systematically applied to other liquid crystal solitons and solitons in other material systems.

Three-dimensional crystals of adaptive knots.

Starting with Gauss and Kelvin, knots in fields were postulated to behave like particles, but experimentally they were found only as transient features or required complex boundary conditions to exist and could not self-assemble into three-dimensional crystals. We introduce energetically stable, micrometer-sized knots in helical fields of chiral liquid crystals. While spatially localized and freely diffusing in all directions, they resemble colloidal particles and atoms, self-assembling into crystalline lattices with open and closed structures. These knots are robust and topologically distinct from the host medium, though they can be morphed and reconfigured by weak stimuli under conditions such as those in displays. A combination of energy-minimizing numerical modeling and optical imaging uncovers the internal structure and topology of individual helical field knots and the various hierarchical crystalline organizations that they form.