Chiral ground states of ferroelectric liquid crystals.

Ferroelectric nematic liquid crystals are formed by achiral molecules with large dipole moments. Their three-dimensional orientational order is described as unidirectionally polar. We demonstrate that the ground state of a flat slab of a ferroelectric nematic unconstrained by externally imposed alignment directions is chiral, with left- and right-handed twists of polarization. Although the helicoidal deformations and defect walls that separate domains of opposite handedness increase the elastic energy, the twists reduce the electrostatic energy and become weaker when the material is doped with ions. This work shows that the polar orientational order of molecules could trigger chirality in soft matter with no chemically induced chiral centers.

Physical insights into biological memory using phospholipid membranes.

Electrical signals may propagate along neuronal membranes in the brain, thus enabling communication between nerve cells. In doing so, lipid bilayers, fundamental scaffolds of all cell membranes, deform and restructure in response to such electrical activity. These changes impact the electromechanical properties of the membrane, which then physically store biological memory. This memory can exist either over a short or long period of time. Traditionally, biological memory is defined by the strengthening or weakening of transmissions between individual neurons. Here, we show that electrical stimulation may also alter the properties of the lipid membrane, thus pointing toward a novel mechanism for memory storage. Furthermore, based on the analysis of existing electrophysiological data, we study molecular mechanisms underlying the long-term potentiation in phospholipid membranes. Finally, we examine possible relationships between the memory capacitive properties of lipid membranes, neuronal learning, and memory.

Differentiating the roles of proteins and polysomes in nucleoid size homeostasis in Escherichia coli.

A defining feature of the bacterial cytosolic interior is a distinct membrane-less organelle, the nucleoid, that contains the chromosomal DNA. Although increasing experimental evidence indicates that macromolecular crowding is the dominant mechanism for nucleoid formation, it has remained unclear which crowders control nucleoid volume. It is commonly assumed that polyribosomes play a dominant role, yet the volume fraction of soluble proteins in the cytosol is comparable with that of polyribosomes. Here, we develop a free energy-based model for the cytosolic interior of a bacterial cell to distinguish contributions arising from polyribosomes and cytosolic proteins in nucleoid volume control. The parameters of the model are determined from the existing experimental data. We show that, while the polysomes establish the existence of the nucleoid as a distinct phase, the proteins control the nucleoid volume in physiologically relevant conditions. Our model explains experimental findings in Escherichia coli that the nucleoid compaction curves in osmotic shock measurements do not depend on cell growth rate and that dissociation of polysomes in slow growth rates does not lead to significant nucleoid expansion, while the nucleoid phase disappears in fastest growth rates. Furthermore, the model predicts a cross-over in the exclusion of crowders by their linear dimensions from the nucleoid phase: below the cross-over of 30-50 nm, the concentration of crowders in the nucleoid phase decreases linearly as a function of the crowder diameter, while decreasing exponentially above the cross-over size. Our work points to the possibility that bacterial cells maintain nucleoid size and protein concentration homeostasis via feedback in which protein concentration controls nucleoid dimensions and the nucleoid dimensions control protein synthesis rate.

Dynamic Stabilization of Metastable States in Triple-Well Ferroelectric Sn2 P2 S6.

Polarization dynamics in ferroelectric materials is governed by the effective potential energy landscape of the order parameter. The unique aspect of ferroelectrics compared to many other transitions is the possibility of more than two potential wells, leading to complicated energy landscapes with new fundamental and functional properties. Here, direct dynamic evidence is revealed of a triple-well potential in the metal thiophosphate Sn2 P2 S6 compound using multivariate scanning probe microscopy combined with theoretical simulations. The key finding is that the metastable zero polarization state can be accessed through a gradual switching process and is stabilized over a broad range of electric fields. Simulations confirm that the observed zero polarization state originates from a kinetic stabilization of the nonpolar state of the triple-well, as opposed to domain walls. Dynamically, the triple-well of Sn2 P2 S6 becomes equivalent to antiferroelectric hysteresis loops. Therefore, this material combines the robust and well-defined domain structure of a proper ferroelectric with dynamic hysteresis loops present in antiferroelectrics. Moreover, the triple-well enhances mem-capacitive effects in Sn2 P2 S6 , which are forbidden for ideal double-well ferroelectrics. These findings provide a path to tunable electronic elements for beyond binary high-density computing devices and neuromorphic circuits based on dynamic properties of the triple-well.

Soliton walls paired by polar surface interactions in a ferroelectric nematic liquid crystal.

Surface interactions are responsible for many properties of condensed matter, ranging from crystal faceting to the kinetics of phase transitions. Usually, these interactions are polar along the normal to the interface and apolar within the interface. Here we demonstrate that polar in-plane surface interactions of a ferroelectric nematic NF produce polar monodomains in micron-thin planar cells and stripes of an alternating electric polarization, separated by [Formula: see text] domain walls, in thicker slabs. The surface polarity binds together pairs of these walls, yielding a total polarization rotation by [Formula: see text]. The polar contribution to the total surface anchoring strength is on the order of 10%. The domain walls involve splay, bend, and twist of the polarization. The structure suggests that the splay elastic constant is larger than the bend modulus. The [Formula: see text] pairs resemble domain walls in cosmology models with biased vacuums and ferromagnets in an external magnetic field.

Survival in branching cellular populations.

We analyze evolutionary dynamics in a confluent, branching cellular population, such as in a growing duct, vasculature, or in a branching microbial colony. We focus on the coarse-grained features of the evolution and build a statistical model that captures the essential features of the dynamics. Using simulations and analytic approaches, we show that the survival probability of strains within the growing population is sensitive to the branching geometry: Branch bifurcations enhance survival probability due to an overall population growth (i.e., "inflation"), while branch termination and the small effective population size at the growing branch tips increase the probability of strain extinction. We show that the evolutionary dynamics may be captured on a wide range of branch geometries parameterized just by the branch diameter N0 and branching rate b. We find that the survival probability of neutral cell strains is largest at an "optimal" branching rate, which balances the effects of inflation and branch termination. We find that increasing the selective advantage s of the cell strain mitigates the inflationary effect by decreasing the average time at which the mutant cell fate is determined. For sufficiently large selective advantages, the survival probability of the advantageous mutant decreases monotonically with the branching rate.

Microemulsions in the driven Widom-Rowlinson lattice gas.

An investigation of the two-dimensional Widom-Rowlinson lattice gas under an applied drive uncovered a remarkable nonequilibrium steady state in which uniform stripes (reminiscent of an equilibrium lamellar phase) form perpendicular to the drive direction [R. Dickman and R. K. P. Zia, Phys. Rev. E 97, 062126 (2018)10.1103/PhysRevE.97.062126]. Here we study this model at low particle densities in two and three dimensions, where we find a disordered phase with a characteristic length scale (a "microemulsion") along the drive direction. We develop a continuum theory of this disordered phase to derive a coarse-grained field-theoretic action for the nonequilibrium dynamics. The action has the form of two coupled driven diffusive systems with different characteristic velocities, generated by an interplay between the particle repulsion and the drive. We then show how fluctuation corrections in the field theory may generate the characteristic features of the microemulsion phase, including a peak in the static structure factor corresponding to the characteristic length scale. This work lays the foundation for understanding the stripe phenomenon more generally.

Shape of population interfaces as an indicator of mutational instability in coexisting cell populations.

Cellular populations such as avascular tumors and microbial biofilms may 'invade' or grow into surrounding populations. The invading population is often comprised of a heterogeneous mixture of cells with varying growth rates. The population may also exhibit mutational instabilities, such as a heavy deleterious mutation load in a cancerous growth. We study the dynamics of a heterogeneous, mutating population competing with a surrounding homogeneous population, as one might find in a cancerous invasion of healthy tissue. We find that the shape of the population interface serves as an indicator for the evolutionary dynamics within the heterogeneous population. In particular, invasion front undulations become enhanced when the invading population is near a mutational meltdown transition or when the surrounding 'bystander' population is barely able to reinvade the mutating population. We characterize these interface undulations and the effective fitness of the heterogeneous population in one- and two-dimensional systems.

Double membrane formation in heterogeneous vesicles.

Lipids are capable of forming a variety of structures, including multi-lamellar vesicles. Layered lipid membranes are found in cell organelles, such as autophagosomes and mitochondria. Here, we present a mechanism for the formation of a double-walled vesicle (i.e., two lipid bilayers) from a unilamellar vesicle through the partitioning and phase separation of a small molecule. Using molecular dynamics simulations, we show that double membrane formation proceeds via a nucleation and growth process - i.e., after a critical concentration of the small molecules, a patch of double membrane nucleates and grows to cover the entire vesicle. We discuss the implications of this mechanism and theoretical approaches for understanding the evolution and formation of double membranes.

Phonon-mediated lipid raft formation in biological membranes.

Short-wavelength collective molecular motions, also known as phonons, have recently attracted much interest in revealing dynamic properties of biological membranes through the use of neutron and X-ray scattering, infrared and Raman spectroscopies, and molecular dynamics simulations. Experimentally detecting unique vibrational patterns such as, shear phonon excitations, viscoelastic crossovers, transverse acoustic phonon gaps, and continuous and truncated optical phonon modes in cellular membranes, to name a few, has proven non-trivial. Here, we review recent advances in liquid thermodynamics that have resulted in the development of the phonon theory of liquids. The theory has important predictions regarding the shear vibrational spectra of fluids, namely the emergence of viscoelastic crossovers and transverse acoustic phonon gaps. Furthermore, we show that these vibrational patterns are common in soft (non-crystalline) materials, including, but not limited to liquids, colloids, liquid crystals (mesogens), block copolymers, and biological membranes. The existence of viscoelastic crossovers and acoustic phonon gaps define the self-diffusion properties of cellular membranes and provide a molecular picture of the transient nature of lipid rafts (Bolmatov et al., 2020). Importantly, the timescales (picoseconds) for the formation and dissolution of transient lipid rafts match the lifetime of the formation and breakdown of interfacial water hydrogen bonds. Apart from acoustic propagating phonon modes, biological membranes can also support more energetic non-propagating optical phonon excitations, also known as standing waves or breathing modes. Importantly, optical phonons can be truncated due to the existence of finite size nanodomains made up of strongly correlated lipid-cholesterol molecular pairs. These strongly coupled molecular pairs can serve as nucleation centers for the formation of stable rafts at larger length scales, due to correlations of spontaneous fluctuations (Onsager's regression hypothesis). Finally and importantly, molecular level viscoelastic crossovers, acoustic phonon gaps, and continuous and truncated optical phonon modes may offer insights as to how lipid-lipid and lipid-protein interactions enable biological function.

Lateral heterogeneity and domain formation in cellular membranes.

As early as the development of the fluid mosaic model for cellular membranes, researchers began observing the telltale signs of lateral heterogeneity. Over the decades this has led to the development of the lipid raft hypothesis and the ensuing controversy that has unfolded, as a result. Here, we review the physical concepts behind domain formation in lipid membranes, both of their structural and dynamic origins. This, then leads into a discussion of coarse-grained, phenomenological approaches that describe the wide range of phases associated with lipid lateral heterogeneity. We use these physical concepts to describe the interaction between raft-lipid species, such as long-chain saturated lipids, sphingomyelin, and cholesterol, and non-raft forming lipids, such as those with short acyl chains or unsaturated fatty acids. While debate has persisted on the biological relevance of lipid domains, recent research, described here, continues to identify biological roles for rafts and new experimental approaches have revealed the existence of lipid domains in living systems. Given the recent progress on both the biological and structural aspects of raft formation, the research area of membrane lateral heterogeneity will not only expand, but will continue to produce exciting results.

Artificial pollen walls simulated by the tandem processes of phase separation and self-assembly in vitro.

Despite numerous attempts to elucidate the developmental mechanisms responsible for the observed diversity of pollen and spore walls, the processes involved remained obscure until the structures observed during exine development were recognized as a sequence of self-assembling micellar mesophases. To confirm this, a series of in vitro experiments was undertaken in which exine-like patterns were generated in colloidal mixtures by self-assembly, without any genomic participation. The intention was to test whether all the main types of exine structure could be simulated experimentally. Mixtures of substances, analogous to those involved in microspore development, were left undisturbed while water evaporated and self-assembly occurred. We varied the substances, their combinations and concentrations, and the physical constraints to make the experiments closer to the situation in nature. The resulting dry films were then examined using transmission electron microscopy. A variety of microstructures, simulating the full range of exine types, was obtained by micellar self-assembly. Moreover, the signs of related physicochemical process (i.e. phase separation) were also observed. Simple, energy-efficient, physical-chemical interactions, phase separation and self-assembly, are capable of generating exine-like patterns, providing evidence that these processes share control of exine formation with the well-documented program of gene expression.

Nucleation of antagonistic organisms and cellular competitions on curved, inflating substrates.

We consider the dynamics of spatially distributed, diffusing populations of organisms with antagonistic interactions. These interactions are found on many length scales, ranging from kilometer-scale animal range dynamics with selection against hybrids to micron-scale interactions between poison-secreting microbial populations. We find that the dynamical line tension at the interface between antagonistic organisms suppresses survival probabilities of small clonal clusters: the line tension introduces a critical cluster size that an organism with a selective advantage must achieve before deterministically spreading through the population. We calculate the survival probability as a function of selective advantage δ and antagonistic interaction strength σ. Unlike a simple Darwinian selective advantage, the survival probability depends strongly on the spatial diffusion constant D_{s} of the strains when σ>0, with suppressed survival when both species are more motile. Finally, we study the survival probability of a single mutant cell at the frontier of a growing spherical cluster of cells, such as the surface of an avascular spherical tumor. Both the inflation and curvature of the frontier significantly enhance the survival probability by changing the critical size of the nucleating cell cluster.

Deciphering Melatonin-Stabilized Phase Separation in Phospholipid Bilayers.

Lipid bilayers are fundamental building blocks of cell membranes, which contain the machinery needed to perform a range of biological functions, including cell-cell recognition, signal transduction, receptor trafficking, viral budding, and cell fusion. Importantly, many of these functions are thought to take place in the laterally phase-separated regions of the membrane, commonly known as lipid rafts. Here, we provide experimental evidence for the "stabilizing" effect of melatonin, a naturally occurring hormone produced by the brain's pineal gland, on phase-separated model membranes mimicking the outer leaflet of plasma membranes. Specifically, we show that melatonin stabilizes the liquid-ordered/liquid-disordered phase coexistence over an extended range of temperatures. The melatonin-mediated stabilization effect is observed in both nanometer- and micrometer-sized liposomes using small angle neutron scattering (SANS), confocal fluorescence microscopy, and differential scanning calorimetry. To experimentally detect nanoscopic domains in 50 nm diameter phospholipid vesicles, we developed a model using the Landau-Brazovskii approach that may serve as a platform for detecting the existence of nanoscopic lateral heterogeneities in soft matter and biological materials with spherical and planar geometries.

Pollen Cell Wall Patterns Form from Modulated Phases.

The ornately geometric walls of pollen grains have inspired scientists for decades. We show that the evolved diversity of these patterns is entirely recapitulated by a biophysical model in which an initially uniform polysaccharide layer in the extracellular space, mechanically coupled to the cell membrane, phase separates to a spatially modulated state. Experiments reveal this process occurring in living cells. We observe that in ∼10% of extant species, this phase separation reaches equilibrium during development such that individual pollen grains are identical and perfectly reproducible. About 90% of species undergo an arrest of this process prior to equilibrium such that individual grains are similar but inexact copies. Equilibrium patterns have appeared multiple times during the evolution of seed plants, but selection does not favor these states. This framework for pattern development provides a route to rationalizing the surface textures of other secreted structures, such as cell walls and insect cuticle.

Aspects of nucleation on curved and flat surfaces.

We investigate the energetics of droplets sourced by the thermal fluctuations in a system undergoing a first-order transition. In particular, we confine our studies to two dimensions with explicit calculations in the plane and on the sphere. Using an isoperimetric inequality from the differential geometry literature and a theorem on the inequality's saturation, we show how geometry informs the critical droplet size and shape. This inequality establishes a "mean field" result for nucleated droplets. We then study the effects of fluctuations on the interfaces of droplets in two dimensions, treating the droplet interface as a fluctuating line. We emphasize that care is needed in deriving the line curvature energy from the Landau-Ginzburg energy functional and in interpreting the scalings of the nucleation rate with the size of the droplet. We end with a comparison of nucleation in the plane and on a sphere.

Genetic drift and selection in many-allele range expansions.

We experimentally and numerically investigate the evolutionary dynamics of four competing strains of E. coli with differing expansion velocities in radially expanding colonies. We compare experimental measurements of the average fraction, correlation functions between strains, and the relative rates of genetic domain wall annihilations and coalescences to simulations modeling the population as a one-dimensional ring of annihilating and coalescing random walkers with deterministic biases due to selection. The simulations reveal that the evolutionary dynamics can be collapsed onto master curves governed by three essential parameters: (1) an expansion length beyond which selection dominates over genetic drift; (2) a characteristic angular correlation describing the size of genetic domains; and (3) a dimensionless constant quantifying the interplay between a colony's curvature at the frontier and its selection length scale. We measure these parameters with a new technique that precisely measures small selective differences between spatially competing strains and show that our simulations accurately predict the dynamics without additional fitting. Our results suggest that the random walk model can act as a useful predictive tool for describing the evolutionary dynamics of range expansions composed of an arbitrary number of genotypes with different fitnesses.

Period proliferation in periodic states in cyclically sheared jammed solids.

Athermal disordered systems can exhibit a remarkable response to an applied oscillatory shear: After a relatively few shearing cycles, the system falls into a configuration that had already been visited in a previous cycle. After this point the system repeats its dynamics periodically despite undergoing many particle rearrangements during each cycle. We study the behavior of orbits as we approach the jamming point in simulations of jammed particles subject to oscillatory shear at fixed pressure and zero temperature. As the pressure is lowered, we find that it becomes more common for the system to find periodic states where it takes multiple cycles before returning to a previously visited state. Thus, there is a proliferation of longer periods as the jamming point is approached.

Spatially Constrained Growth Enhances Conversional Meltdown.

Cells that mutate or commit to a specialized function (differentiate) often undergo conversions that are effectively irreversible. Slowed growth of converted cells can act as a form of selection, balancing unidirectional conversion to maintain both cell types at a steady-state ratio. However, when one-way conversion is insufficiently counterbalanced by selection, the original cell type will ultimately be lost, often with negative impacts on the population's overall fitness. The critical balance between selection and conversion needed for preservation of unconverted cells and the steady-state ratio between cell types depends on the spatial circumstances under which cells proliferate. We present experimental data on a yeast strain engineered to undergo irreversible conversion: this synthetic system permits cell-type-specific fluorescent labeling and exogenous variation of the relative growth and conversion rates. We find that populations confined to grow on a flat agar surface are more susceptible than their well-mixed counterparts to fitness loss via a conversion-induced "meltdown." We then present analytical predictions for growth in several biologically relevant geometries-well-mixed liquid media, radially expanding two-dimensional colonies, and linear fronts in two dimensions-by employing analogies to the directed-percolation transition from nonequilibrium statistical physics. These simplified theories are consistent with the experimental results.