The smectic ZA phase: Antiferroelectric smectic order as a prelude to the ferroelectric nematic.

We have structurally characterized the liquid crystal (LC) phase that can appear as an intermediate state when a dielectric nematic, having polar disorder of its molecular dipoles, transitions to the almost perfectly polar-ordered ferroelectric nematic. This intermediate phase, which fills a 100-y-old void in the taxonomy of smectic LCs and which we term the "smectic ZA," is antiferroelectric, with the nematic director and polarization oriented parallel to smectic layer planes, and the polarization alternating in sign from layer to layer with a 180 Å period. A Landau free energy, originally derived from the Ising model of ferromagnetic ordering of spins in the presence of dipole-dipole interactions, and applied to model incommensurate antiferroelectricity in crystals, describes the key features of the nematic-SmZA-ferroelectric nematic phase sequence.

Observation of a uniaxial ferroelectric smectic A phase.

We report the observation of the smectic AF, a liquid crystal phase of the ferroelectric nematic realm. The smectic AF is a phase of small polar, rod-shaped molecules that form two-dimensional fluid layers spaced by approximately the mean molecular length. The phase is uniaxial, with the molecular director, the local average long-axis orientation, normal to the layer planes, and ferroelectric, with a spontaneous electric polarization parallel to the director. Polarization measurements indicate almost complete polar ordering of the ∼10 Debye longitudinal molecular dipoles, and hysteretic polarization reversal with a coercive field ∼2 × 105 V/m is observed. The SmAF phase appears upon cooling in two binary mixtures of partially fluorinated mesogens: 2N/DIO, exhibiting a nematic (N)-smectic ZA (SmZA)-ferroelectric nematic (NF)-SmAF phase sequence, and 7N/DIO, exhibiting an N-SmZA-SmAF phase sequence. The latter presents an opportunity to study a transition between two smectic phases having orthogonal systems of layers.

Toward the cellular-scale simulation of motor-driven cytoskeletal assemblies.

The cytoskeleton - a collection of polymeric filaments, molecular motors, and crosslinkers - is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here, we present aLENS (a Living Ensemble Simulator), a novel computational framework designed to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the system dynamics while efficiently and stably enforcing hard-body repulsion between filaments. Molecular potentials are entirely avoided in imposing steric constraints. Utilizing parallel computing, we simulate tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating emergent phenomena such as bundle formation and buckling. This simulation framework can help elucidate how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of cytoskeletal active matter.

Active condensation of filaments under spatial confinement.

Living systems exhibit self-organization, a phenomenon that enables organisms to perform functions essential for life. The interior of living cells is a crowded environment in which the self-assembly of cytoskeletal networks is spatially constrained by membranes and organelles. Cytoskeletal filaments undergo active condensation in the presence of crosslinking motor proteins. In past studies, confinement has been shown to alter the morphology of active condensates. Here, we perform simulations to explore systems of filaments and crosslinking motors in a variety of confining geometries. We simulate spatial confinement imposed by hard spherical, cylindrical, and planar boundaries. These systems exhibit non-equilibrium condensation behavior where crosslinking motors condense a fraction of the overall filament population, leading to coexistence of vapor and condensed states. We find that the confinement lengthscale modifies the dynamics and condensate morphology. With end-pausing crosslinking motors, filaments self-organize into half asters and fully-symmetric asters under spherical confinement, polarity-sorted bilayers and bottle-brush-like states under cylindrical confinement, and flattened asters under planar confinement. The number of crosslinking motors controls the size and shape of condensates, with flattened asters becoming hollow and ring-like for larger motor number. End pausing plays a key role affecting condensate morphology: systems with end-pausing motors evolve into aster-like condensates while those with non-end-pausing crosslinking motor proteins evolve into disordered clusters and polarity-sorted bundles.

Chiral self-sorting of active semiflexible filaments with intrinsic curvature.

Many-body interactions in systems of active matter can cause particles to move collectively and self-organize into dynamic structures with long-range order. In cells, the self-assembly of cytoskeletal filaments is critical for cellular motility, structure, intracellular transport, and division. Semiflexible cytoskeletal filaments driven by polymerization or motor-protein interactions on a two-dimensional substrate, such as the cell cortex, can induce filament bending and curvature leading to interesting collective behavior. For example, the bacterial cell-division filament FtsZ is known to have intrinsic curvature that causes it to self-organize into rings and vortices, and recent experiments reconstituting the collective motion of microtubules driven by motor proteins on a surface have observed chiral symmetry breaking of the collective behavior due to motor-induced curvature of the filaments. Previous work on the self-organization of driven filament systems have not studied the effects of curvature and filament structure on collective behavior. In this work, we present Brownian dynamics simulation results of driven semiflexible filaments with intrinsic curvature and investigate how the interplay between filament rigidity and radius of curvature can tune the self-organization behavior in homochiral systems and heterochiral mixtures. We find a curvature-induced reorganization from polar flocks to self-sorted chiral clusters, which is modified by filament flexibility. This transition changes filament transport from ballistic to diffusive at long timescales.

Polar in-plane surface orientation of a ferroelectric nematic liquid crystal: Polar monodomains and twisted state electro-optics.

We show that surface interactions can vectorially structure the three-dimensional polarization field of a ferroelectric fluid. The contact between a ferroelectric nematic liquid crystal and a surface with in-plane polarity generates a preferred in-plane orientation of the polarization field at that interface. This is a route to the formation of fluid or glassy monodomains of high polarization without the need for electric field poling. For example, unidirectional buffing of polyimide films on planar surfaces to give quadrupolar in-plane anisotropy also induces macroscopic in-plane polar order at the surfaces, enabling the formation of a variety of azimuthal polar director structures in the cell interior, including uniform and twisted states. In a π-twist cell, obtained with antiparallel, unidirectional buffing on opposing surfaces, we demonstrate three distinct modes of ferroelectric nematic electro-optic response: intrinsic, viscosity-limited, field-induced molecular reorientation; field-induced motion of domain walls separating twisted states of opposite chirality; and propagation of polarization reorientation solitons from the cell plates to the cell center upon field reversal. Chirally doped ferroelectric nematics in antiparallel-rubbed cells produce Grandjean textures of helical twist that can be unwound via field-induced polar surface reorientation transitions. Fields required are in the 3-V/mm range, indicating an in-plane polar anchoring energy of w P ∼3 × 10-3 J/m2.

Comparison of explicit and mean-field models of cytoskeletal filaments with crosslinking motors.

In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor-filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor-filament interactions are needed. Here, we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by [Formula: see text]-[Formula: see text] compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor-filament networks on micrometer to millimeter length scales.

Collective motion of driven semiflexible filaments tuned by soft repulsion and stiffness.

In active matter systems, self-propelled particles can self-organize to undergo collective motion, leading to persistent dynamical behavior out of equilibrium. In cells, cytoskeletal filaments and motor proteins form complex structures important for cell mechanics, motility, and division. Collective dynamics of cytoskeletal systems can be reconstituted using filament gliding experiments, in which cytoskeletal filaments are propelled by surface-bound motor proteins. These experiments have observed diverse dynamical states, including flocks, polar streams, swirling vortices, and single-filament spirals. Recent experiments with microtubules and kinesin motor proteins found that the collective behavior of gliding filaments can be tuned by altering the concentration of the crowding macromolecule methylcellulose in solution. Increasing the methylcellulose concentration reduced filament crossing, promoted alignment, and led to a transition from active, isotropically oriented filaments to locally aligned polar streams. This emergence of collective motion is typically explained as an increase in alignment interactions by Vicsek-type models of active polar particles. However, it is not yet understood how steric interactions and bending stiffness modify the collective behavior of active semiflexible filaments. Here we use simulations of driven filaments with tunable soft repulsion and rigidity in order to better understand how the interplay between filament flexibility and steric effects can lead to different active dynamic states. We find that increasing filament stiffness decreases the probability of filament alignment, yet increases collective motion and long-range order, in contrast to the assumptions of a Vicsek-type model. We identify swirling flocks, polar streams, buckling bands, and spirals, and describe the physics that govern transitions between these states. In addition to repulsion and driving, tuning filament stiffness can promote collective behavior, and controls the transition between active isotropic filaments, locally aligned flocks, and polar streams.

First-principles experimental demonstration of ferroelectricity in a thermotropic nematic liquid crystal: Polar domains and striking electro-optics.

We report the experimental determination of the structure and response to applied electric field of the lower-temperature nematic phase of the previously reported calamitic compound 4-[(4-nitrophenoxy)carbonyl]phenyl2,4-dimethoxybenzoate (RM734). We exploit its electro-optics to visualize the appearance, in the absence of applied field, of a permanent electric polarization density, manifested as a spontaneously broken symmetry in distinct domains of opposite polar orientation. Polarization reversal is mediated by field-induced domain wall movement, making this phase ferroelectric, a 3D uniaxial nematic having a spontaneous, reorientable polarization locally parallel to the director. This polarization density saturates at a low temperature value of ∼6 µC/cm2, the largest ever measured for a fluid or glassy material. This polarization is comparable to that of solid state ferroelectrics and is close to the average value obtained by assuming perfect, polar alignment of molecular dipoles in the nematic. We find a host of spectacular optical and hydrodynamic effects driven by ultralow applied field (E ∼ 1 V/cm), produced by the coupling of the large polarization to nematic birefringence and flow. Electrostatic self-interaction of the polarization charge renders the transition from the nematic phase mean field-like and weakly first order and controls the director field structure of the ferroelectric phase. Atomistic molecular dynamics simulation reveals short-range polar molecular interactions that favor ferroelectric ordering, including a tendency for head-to-tail association into polar, chain-like assemblies having polar lateral correlations. These results indicate a significant potential for transformative, new nematic physics, chemistry, and applications based on the enhanced understanding, development, and exploitation of molecular electrostatic interaction.

Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling.

The essential functions required for mitotic spindle assembly and chromosome biorientation and segregation are not fully understood, despite extensive study. To illuminate the combinations of ingredients most important to align and segregate chromosomes and simultaneously assemble a bipolar spindle, we developed a computational model of fission-yeast mitosis. Robust chromosome biorientation requires progressive restriction of attachment geometry, destabilization of misaligned attachments, and attachment force dependence. Large spindle length fluctuations can occur when the kinetochore-microtubule attachment lifetime is long. The primary spindle force generators are kinesin-5 motors and crosslinkers in early mitosis, while interkinetochore stretch becomes important after biorientation. The same mechanisms that contribute to persistent biorientation lead to segregation of chromosomes to the poles after anaphase onset. This model therefore provides a framework to interrogate key requirements for robust chromosome biorientation, spindle length regulation, and force generation in the spindle.

Before a cell divides, it must make a copy of its genetic material and then promptly split in two. This process, called mitosis, is coordinated by many different molecular machines. The DNA is copied, then the duplicated chromosomes line up at the middle of the cell. Next, an apparatus called the mitotic spindle latches onto the chromosomes before pulling them apart. The mitotic spindle is a bundle of long, thin filaments called microtubules. It attaches to chromosomes at the kinetochore, the point where two copied chromosomes are cinched together in their middle. Proper cell division is vital for the healthy growth of all organisms, big and small, and yet some parts of the process remain poorly understood despite extensive study. Specifically, there is more to learn about how the mitotic spindle self-assembles, and how microtubules and kinetochores work together to correctly orient and segregate chromosomes into two sister cells. These nanoscale processes are happening a hundred times a minute, so computer simulations are a good way to test what we know. Edelmaier et al. developed a computer model to simulate cell division in fission yeast, a species of yeast often used to study fundamental processes in the cell. The model simulates how the mitotic spindle assembles, how its microtubules attach to the kinetochore and the force required to pull two sister chromosomes apart. Building the simulation involved modelling interactions between the mitotic spindle and kinetochore, their movement and forces applied. To test its accuracy, model simulations were compared to recordings of the mitotic spindle ­ including its length, structure and position ­ imaged from dividing yeast cells. Running the simulation, Edelmaier et al. found that several key effects are essential for the proper movement of chromosomes in mitosis. This includes holding chromosomes in the correct orientation as the mitotic spindle assembles and controlling the relative position of microtubules as they attach to the kinetochore. Misaligned attachments must also be readily deconstructed and corrected to prevent any errors. The simulations also showed that kinetochores must begin to exert more force (to separate the chromosomes) once the mitotic spindle is attached correctly. Altogether, these findings improve the current understanding of how the mitotic spindle and its counterparts control cell division. Errors in chromosome segregation are associated with birth defects and cancer in humans, and this new simulation could potentially now be used to help make predictions about how to correct mistakes in the process.

End-to-end machine learning for experimental physics: using simulated data to train a neural network for object detection in video microscopy.

We demonstrate a method for training a convolutional neural network with simulated images for usage on real-world experimental data. Modern machine learning methods require large, robust training data sets to generate accurate predictions. Generating these large training sets requires a significant up-front time investment that is often impractical for small-scale applications. Here we demonstrate a 'full-stack' computational solution, where the training data set is generated on-the-fly using a noise injection process to produce simulated data characteristic of the experimental system. We demonstrate the power of this full-stack approach by applying it to the study of topological defect annihilation in systems of liquid crystal freely-suspended films. This specific experimental system requires accurate observations of both the spatial distribution of the defects and the total number of defects, making it an ideal system for testing the robustness of the trained network. The fully trained network was found to be comparable in accuracy to human hand-annotation, with four-orders of magnitude improvement in time efficiency.

Frustration between two- and three-dimensional smectic ordering leads to a biaxial nematic phase.

The bola-amphiphilic, T-shaped mesogen CT2 has an aromatic, biphenyl core terminated on both ends by hydrophilic groups and a semi-perfluorinated, aliphatic side chain. Upon cooling from the isotropic phase, the fluorinated tails and the polar, rod-like cores nanophase-segregate to form a fluid lamellar phase. At high temperatures, the biphenyl cores are orientationally disordered in two dimensions (2D) in the lamellar planes but on further cooling the cores order orientationally, giving a biaxial lamellar phase with 2D nematic in-plane ordering. At lower temperature, the aromatic and hydrophilic parts of the cores nanosegregate within the lamellae and 2D smectic correlations of the head groups develop. X-ray diffraction shows that this 2D smectic ordering is incompatible with the initial lamellar structure, with both structures becoming short-ranged, resulting in a 3D biaxial nematic phase with macroscopic orthorhombic symmetry featuring strong smectic correlations in two orthogonal spatial dimensions. Freeze-fracture transmission electron microscopy enables direct visualization of the resulting short-ranged periodic structures.

Theory of Cytoskeletal Reorganization during Cross-Linker-Mediated Mitotic Spindle Assembly.

Cells grow, move, and respond to outside stimuli by large-scale cytoskeletal reorganization. A prototypical example of cytoskeletal remodeling is mitotic spindle assembly, during which microtubules nucleate, undergo dynamic instability, bundle, and organize into a bipolar spindle. Key mechanisms of this process include regulated filament polymerization, cross-linking, and motor-protein activity. Remarkably, using passive cross-linkers, fission yeast can assemble a bipolar spindle in the absence of motor proteins. We develop a torque-balance model that describes this reorganization because of dynamic microtubule bundles, spindle-pole bodies, the nuclear envelope, and passive cross-linkers to predict spindle-assembly dynamics. We compare these results to those obtained with kinetic Monte Carlo-Brownian dynamics simulations, which include cross-linker-binding kinetics and other stochastic effects. Our results show that rapid cross-linker reorganization to microtubule overlaps facilitates cross-linker-driven spindle assembly, a testable prediction for future experiments. Combining these two modeling techniques, we illustrate a general method for studying cytoskeletal network reorganization.

Chiral Incommensurate Helical Phase in a Smectic of Achiral Bent-Core Mesogens.

An achiral, bent-core mesogen forms several tilted smectic liquid crystal phases, including a nonpolar, achiral de Vries smectic A which transitions to a chiral, ferroelectric state in applied electric fields above a threshold. At lower temperature, a chiral, ferrielectric phase with a periodic, supermolecular modulation of the tilt azimuth, indicated by a Bragg peak in carbon-edge resonant soft x-ray scattering, is observed. The absence of a corresponding resonant umklapp peak identifies the superlayer structure as a twist-bend-like helix that is only weakly modulated by the smectic layering.

Understanding the Nanoscale Structure of Inverted Hexagonal Phase Lyotropic Liquid Crystal Polymer Membranes.

Periodic, nanostructured porous polymer membranes made from the cross-linked inverted hexagonal phase of self-assembled lyotropic liquid crystals (LLCs) are a promising class of materials for selective separations. In this work, we investigate an experimentally characterized LLC polymer membrane using atomistic molecular modeling. In particular, we compare simulated X-ray diffraction (XRD) patterns with experimental XRD data to quantify and understand the differences between simulation and experiment. We find that the nanopores are likely composed of five columns of stacked LLC monomers which surround each hydrophilic core. Evidence suggests that these columns likely move independently of each other over longer time scales than accessible via atomistic simulation. We also find that wide-angle X-ray scattering structural features previously attributed to monomer tail tilt are likely instead due to ordered tail packing. Although this system has been reported as dry, we show that small amounts of water are necessary to reproduce all features from the experimental XRD pattern because of asymmetries introduced by hydrogen bonds between the monomer head groups and water molecules. Finally, we explore the composition and structure of the nanopores and reveal that there exists a composition gradient rather than an abrupt partition between the hydrophilic and hydrophobic regions. A caveat is that the time scales of the dynamics are extremely long for this system, resulting in simulated structures that appear too ordered, thus requiring careful examination of the metastable states observed in order to draw any conclusions. The clear picture of the nanoscopic structure of these membranes provided in this study will enable a better understanding of the mechanisms of small-molecule transport within these nanopores.

New SmAPF Mesogens Designed for Analog Electrooptics Applications.

We have previously reported the first realization of an orthogonal ferroelectric bent-core SmAPF phase by directed design in mesogens with a single tricarbosilane-terminated alkoxy tail. Given the potentially useful electrooptic properties of this phase, including analog phase-only electrooptic index modulation with optical latching, we have been exploring its "structure space", searching for novel SmAPF mesogens. Here, we report two classes of these-the first designed to optimize the dynamic range of the index modulation in parallel-aligned cells by lowering the bend angle of the rigid core, and the second expanding the structure space of the phase by replacing the tricarbosilane-terminated alkyl tail with a polyfluorinated polyethylene glycol oligomer.

Two-dimensional island emulsions in ultrathin, freely-suspended smectic liquid crystal films.

We report a novel type of two-dimensional colloidal emulsion, in which arrays of disc-shaped liquid crystal domains are created in ultrathin, freely-suspended, fluid smectic C liquid crystal films. After a film has been drawn across an aperture, an island emulsion is produced by repeatedly compressing and expanding the film while maintaining vigorous shear and extensional air flow across its area. Once formed, these emulsions restructure over a period of a few minutes to a stable state that then changes only slowly, over the course of several days. This stability enables study of the sedimentation of the emulsion under in-plane gravitation produced by tilting the film, during which the original island emulsion segregates into regions with different kinds of emulsions distinguished by the size, density, and degree of order of the islands. We observe a rich array of phenomena that includes the formation of chains of islands organized into two-dimensional smectics in the dilute phase, and island deformation and coalescence in the condensed phase.

Effect of Conformational Chirality on Optical Activity Observed in a Smectic of Achiral, Bent-Core Molecules.

Smectics of achiral, tilted bent-core liquid crystal molecules are chiral, but their optical activity is generally small. Here, we study the effect of conformational chirality on optical activity in smectic phases of an achiral, bent-core mesogen, W513. The neat material has a modulated B4 phase, which appears dark under crossed polarizers and shows no observable optical rotation under decrossed polarizers. However, mixtures of W513 with a rod-like mesogen, 8CB, show a conventional B4 phase, in which distinct left- and right-handed chiral domains with opposite optical activity are observed. The optical behavior of the mixtures is consistent with NMR results, which show a splitting of the carbonyl peak of the bent-core molecules into two, indicating a twisted conformation between the two molecular arms of the bent-core molecules as in conventional B4 materials.

Understanding the origin of liquid crystal ordering of ultrashort double-stranded DNA.

Recent experiments have shown that short double-stranded DNA (dsDNA) fragments having six- to 20-base pairs exhibit various liquid crystalline phases. This violates the condition of minimum molecular shape anisotropy that analytical theories demand for liquid crystalline ordering. It has been hypothesized that the liquid crystalline ordering is the result of end-to-end stacking of dsDNA to form long supramolecular columns which satisfy the shape anisotropy criterion necessary for ordering. To probe the thermodynamic feasibility of this process, we perform molecular dynamics simulations on ultrashort (four base pair long) dsDNA fragments, quantify the strong end-to-end attraction between them, and demonstrate that the nematic ordering of the self-assembled stacked columns is retained for a large range of temperature and salt concentration.

Active microrheology of smectic membranes.

Thin fluid membranes embedded in a bulk fluid of different viscosity are of fundamental interest as experimental realizations of quasi-two-dimensional fluids and as models of biological membranes. We have probed the hydrodynamics of thin fluid membranes by active microrheology using small tracer particles to observe the highly anisotropic flow fields generated around a rigid oscillating post inserted into a freely suspended smectic liquid crystal film that is surrounded by air. In general, at distances more than a few Saffman lengths from the meniscus around the post, the measured velocities are larger than the flow computed by modeling a moving disklike inclusion of finite extent by superposing Levine-MacKintosh response functions for pointlike inclusions in a viscous membrane. The observed discrepancy is attributed to additional coupling of the film with the air below the film that is displaced directly by the shaft of the moving post.