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.

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.

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.

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.

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.

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.

First-order patterning transitions on a sphere as a route to cell morphology.

We propose a general theory for surface patterning in many different biological systems, including mite and insect cuticles, pollen grains, fungal spores, and insect eggs. The patterns of interest are often intricate and diverse, yet an individual pattern is robustly reproducible by a single species and a similar set of developmental stages produces a variety of patterns. We argue that the pattern diversity and reproducibility may be explained by interpreting the pattern development as a first-order phase transition to a spatially modulated phase. Brazovskii showed that for such transitions on a flat, infinite sheet, the patterns are uniform striped or hexagonal. Biological objects, however, have finite extent and offer different topologies, such as the spherical surfaces of pollen grains. We consider Brazovskii transitions on spheres and show that the patterns have a richer phenomenology than simple stripes or hexagons. We calculate the free energy difference between the unpatterned state and the many possible patterned phases, taking into account fluctuations and the system's finite size. The proliferation of variety on a sphere may be understood as a consequence of topology, which forces defects into perfectly ordered phases. The defects are then accommodated in different ways. We also argue that the first-order character of the transition is responsible for the reproducibility and robustness of the pattern formation.

Lassoing saddle splay and the geometrical control of topological defects.

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.

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.

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.

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.

Survival probabilities at spherical frontiers.

Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with an arbitrary power-law in time: R(t) = R0(1 + t/t(∗))Θ, where Θ is a growth exponent, R0 is the initial radius, and t(∗) is a characteristic time for the growth, to be affected by the inflating geometry. We vary the parameters t(∗) and Θ to capture a variety of possible growth regimes. Guided by recent results for two-dimensional inflating range expansions, we identify key dimensionless parameters that describe the survival probability of a mutant cell with a small selective advantage arising at the population frontier. Using analytical techniques, we calculate this probability for arbitrary Θ. We compare our results to simulations of linearly inflating expansions (Θ = 1 spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) and treadmilling populations (Θ = 0, with cells in the interior removed by apoptosis or a similar process). We find that mutations at linearly inflating fronts have survival probabilities enhanced by factors of 100 or more relative to mutations at treadmilling population frontiers. We also discuss the special properties of "marginally inflating" (Θ = 1/2) expansions.

Asymmetric mutualism in two- and three-dimensional range expansions.

Genetic drift at the frontiers of two-dimensional range expansions of microorganisms can frustrate local cooperation between different genetic variants, demixing the population into distinct sectors. In a biological context, mutualistic or antagonistic interactions will typically be asymmetric between variants. By taking into account both the asymmetry and the interaction strength, we show that the much weaker demixing in three dimensions allows for a mutualistic phase over a much wider range of asymmetric cooperative benefits, with mutualism prevailing for any positive, symmetric benefit. We also demonstrate that expansions with undulating fronts roughen dramatically at the boundaries of the mutualistic phase, with severe consequences for the population genetics along the transition lines.

Trapping of isotropic droplets by disclinations in nematic liquid crystals controlled by surface anchoring and elastic constant disparity.

Linear defects such as dislocations and disclinations in ordered materials attract foreign particles since they replace strong elastic distortions at the defect cores. In this work, we explore the behavior of isotropic droplets nucleating at singular disclinations in a nematic liquid crystal, predesigned by surface photopatterning. Experiments show that in the biphasic nematic-isotropic region, although the droplets are attracted to the disclination cores, their centers of mass shift away from the core centers as the temperature increases. The shift is not random, being deterministically defined by the surrounding director field. The effect is explained by the balance of interfacial anchoring and bulk elasticity. An agreement with the experiment can be achieved only if the model accounts for the disparity of the nematic elastic constants; the so-called one-constant approximation, often used in the theoretical analysis of liquid crystals, produces qualitatively wrong predictions. In particular, the experimentally observed shift towards the bend region around a +1/2 disclination core can be explained only when the bend constant is larger than the splay constant. The described dependence of the precise location of a foreign inclusion at defect cores on the elastic and surface anchoring properties can be used in rational design of microscale architectures.

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.

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.

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.