Condensate interfacial forces reposition DNA loci and probe chromatin viscoelasticity.

Biomolecular condensates assemble in living cells through phase separation and related phase transitions. An underappreciated feature of these dynamic molecular assemblies is that they form interfaces with other cellular structures, including membranes, cytoskeleton, DNA and RNA, and other membraneless compartments. These interfaces are expected to give rise to capillary forces, but there are few ways of quantifying and harnessing these forces in living cells. Here, we introduce viscoelastic chromatin tethering and organization (VECTOR), which uses light-inducible biomolecular condensates to generate capillary forces at targeted DNA loci. VECTOR can be utilized to programmably reposition genomic loci on a timescale of seconds to minutes, quantitatively revealing local heterogeneity in the viscoelastic material properties of chromatin. These synthetic condensates are built from components that naturally form liquid-like structures in living cells, highlighting the potential role for native condensates to generate forces and do work to reorganize the genome and impact chromatin architecture.

Synergistic and antagonistic effects of deterministic and stochastic cell-cell variations.

By diversifying, cells in a clonal population can together overcome the limits of individuals. Diversity in single-cell growth rates allows the population to survive environmental stresses, such as antibiotics, and grow faster than the undiversified population. These functional cell-cell variations can arise stochastically, from noise in biochemical reactions, or deterministically, by asymmetrically distributing damaged components. While each of the mechanisms is well understood, the effect of the combined mechanisms is unclear. To evaluate the contribution of the deterministic component we developed a mathematical model by mapping the growing population to the Ising model. To analyze the combined effects of stochastic and deterministic contributions we introduced the analytical results of the Ising-mapping into an Euler-Lotka framework. Model results, confirmed by simulations and experimental data, show that deterministic cell-cell variations increase near-linearly with stress. As a consequence, we predict that the gain in population doubling time from cell-cell variations is primarily stochastic at low stress but may cross over to deterministic at higher stresses. Furthermore, we find that while the deterministic component minimizes population damage, stochastic variations antagonize this effect. Together our results may help identifying stress-tolerant pathogenic cells and thus inspire novel antibiotic strategies.

Obstructed swelling and fracture of hydrogels.

Obstructions influence the growth and expansion of bodies in a wide range of settings-but isolating and understanding their impact can be difficult in complex environments. Here, we study obstructed growth/expansion in a model system accessible to experiments, simulations, and theory: hydrogels swelling around fixed cylindrical obstacles with varying geometries. When the obstacles are large and widely-spaced, hydrogels swell around them and remain intact. In contrast, our experiments reveal that when the obstacles are narrow and closely-spaced, hydrogels fracture as they swell. We use finite element simulations to map the magnitude and spatial distribution of stresses that build up during swelling at equilibrium in a 2D model, providing a route toward predicting when this phenomenon of self-fracturing is likely to arise. Applying lessons from indentation theory, poroelasticity, and nonlinear continuum mechanics, we also develop a theoretical framework for understanding how the maximum principal tensile and compressive stresses that develop during swelling are controlled by obstacle geometry and material parameters. These results thus help to shed light on the mechanical principles underlying growth/expansion in environments with obstructions.

Mechanical constraints to unbound expansion of B. subtilis on semi-solid surfaces.

IMPORTANCE: How bacterial cells colonize new territory is a problem of fundamental microbiological and biophysical interest and is key to the emergence of several phenomena of biological, ecological, and medical relevance. Here, we demonstrate how bacteria stuck in a colony of finite size can resume exploration of new territory by aquaplaning and how they fine tune biofilm viscoelasticity to surface material properties that allows them differential mobility. We show how changing local interfacial forces and colony viscosity results in a plethora of bacterial morphologies on surfaces with different physical and mechanical properties.

Liquid-liquid phase separation within fibrillar networks.

Complex fibrillar networks mediate liquid-liquid phase separation of biomolecular condensates within the cell. Mechanical interactions between these condensates and the surrounding networks are increasingly implicated in the physiology of the condensates and yet, the physical principles underlying phase separation within intracellular media remain poorly understood. Here, we elucidate the dynamics and mechanics of liquid-liquid phase separation within fibrillar networks by condensing oil droplets within biopolymer gels. We find that condensates constrained within the network pore space grow in abrupt temporal bursts. The subsequent restructuring of condensates and concomitant network deformation is contingent on the fracture of network fibrils, which is determined by a competition between condensate capillarity and network strength. As a synthetic analog to intracellular phase separation, these results further our understanding of the mechanical interactions between biomolecular condensates and fibrillar networks in the cell.

Chemotactic Motility-Induced Phase Separation.

Collectives of actively moving particles can spontaneously separate into dilute and dense phases-a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS-in some cases, arresting or completely suppressing phase separation, or in other cases, generating fundamentally new dynamic instabilities. We establish principles describing this competition, thereby helping to reveal and clarify the rich physics underlying active matter systems that perform chemotaxis, ranging from cells to robots.

Flows of a nonequilibrated aqueous two-phase system in a microchannel.

Liquid-liquid phase separation is a rich and dynamic process, which recently has gained new interest, especially in biology and for material synthesis. In this work, we experimentally show that co-flow of a nonequilibrated aqueous two-phase system within a planar flow-focusing microfluidic device results in a three-dimensional flow, as the two nonequilibrated solutions move downstream along the length of the microchannel. After the system reaches steady-state, invasion fronts from the outer stream are formed along the top and bottom walls of the microfluidic device. The invasion fronts advance towards the center of the channel, until they merge. We first show by tuning the concentration of polymer species within the system that the formation of these fronts is due to liquid-liquid phase separation. Moreover, the rate of invasion from the outer stream increases with increasing polymer concentrations in the streams. We hypothesize the invasion front formation and growth is driven by Marangoni flow induced by the polymer concentration gradient along the width of the channel, as the system is undergoing phase separation. In addition, we show how at various downstream positions the system reaches its steady-state configuration once the two fluid streams flow side-by-side in the channel.

Self-assembly of tessellated tissue sheets by expansion and collision.

Tissues do not exist in isolation-they interact with other tissues within and across organs. While cell-cell interactions have been intensely investigated, less is known about tissue-tissue interactions. Here, we studied collisions between monolayer tissues with different geometries, cell densities, and cell types. First, we determine rules for tissue shape changes during binary collisions and describe complex cell migration at tri-tissue boundaries. Next, we propose that genetically identical tissues displace each other based on pressure gradients, which are directly linked to gradients in cell density. We present a physical model of tissue interactions that allows us to estimate the bulk modulus of the tissues from collision dynamics. Finally, we introduce TissEllate, a design tool for self-assembling complex tessellations from arrays of many tissues, and we use cell sheet engineering techniques to transfer these composite tissues like cellular films. Overall, our work provides insight into the mechanics of tissue collisions, harnessing them to engineer tissue composites as designable living materials.

Linear viscoelastic properties of the vertex model for epithelial tissues.

Epithelial tissues act as barriers and, therefore, must repair themselves, respond to environmental changes and grow without compromising their integrity. Consequently, they exhibit complex viscoelastic rheological behavior where constituent cells actively tune their mechanical properties to change the overall response of the tissue, e.g., from solid-like to fluid-like. Mesoscopic mechanical properties of epithelia are commonly modeled with the vertex model. While previous studies have predominantly focused on the rheological properties of the vertex model at long time scales, we systematically studied the full dynamic range by applying small oscillatory shear and bulk deformations in both solid-like and fluid-like phases for regular hexagonal and disordered cell configurations. We found that the shear and bulk responses in the fluid and solid phases can be described by standard spring-dashpot viscoelastic models. Furthermore, the solid-fluid transition can be tuned by applying pre-deformation to the system. Our study provides insights into the mechanisms by which epithelia can regulate their rich rheological behavior.

Transmural pressure signals through retinoic acid to regulate lung branching.

During development, the mammalian lung undergoes several rounds of branching, the rate of which is tuned by the relative pressure of the fluid within the lumen of the lung. We carried out bioinformatics analysis of RNA-sequencing of embryonic mouse lungs cultured under physiologic or sub-physiologic transmural pressure and identified transcription factor-binding motifs near genes whose expression changes in response to pressure. Surprisingly, we found retinoic acid (RA) receptor binding sites significantly overrepresented in the promoters and enhancers of pressure-responsive genes. Consistently, increasing transmural pressure activates RA signaling, and pharmacologically inhibiting RA signaling decreases airway epithelial branching and smooth muscle wrapping. We found that pressure activates RA signaling through the mechanosensor Yap. A computational model predicts that mechanical signaling through Yap and RA affects lung branching by altering the balance between epithelial proliferation and smooth muscle wrapping, which we test experimentally. Our results reveal that transmural pressure signals through RA to balance the relative rates of epithelial growth and smooth muscle differentiation in the developing mouse lung and identify RA as a previously unreported component in the mechanotransduction machinery of embryonic tissues.

Stress ball morphogenesis: How the lizard builds its lung.

The function of the lung is closely coupled to its structural anatomy, which varies greatly across vertebrates. Although architecturally simple, a complex pattern of airflow is thought to be achieved in the lizard lung due to its cavernous central lumen and honeycomb-shaped wall. We find that the wall of the lizard lung is generated from an initially smooth epithelial sheet, which is pushed through holes in a hexagonal smooth muscle meshwork by forces from fluid pressure, similar to a stress ball. Combining transcriptomics with time-lapse imaging reveals that the hexagonal meshwork self-assembles in response to circumferential and axial stresses downstream of pressure. A computational model predicts the pressure-driven changes in epithelial topology, which we probe using optogenetically driven contraction of 3D-printed engineered muscle. These results reveal the physical principles used to sculpt the unusual architecture of the lizard lung, which could be exploited as a novel strategy to engineer tissues.

Method of image charges for describing deformation of bounded two-dimensional solids with circular inclusions.

We present a method for predicting the linear response deformation of finite and semi-infinite 2D solid structures with circular holes and inclusions by employing the analogies with image charges and induction in electrostatics. Charges in electrostatics induce image charges near conductive boundaries and an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects. Similarly, charges in elasticity induce image charges near boundaries and external stress induces polarization (quadrupoles and other multipoles) inside holes and inclusions. Stresses generated by these induced elastic multipoles as well as stresses generated by their images near boundaries then lead to interactions between holes and inclusions and with their images, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external field, between them, and with their images. The results of our method for linear deformation of circular holes and inclusions near straight and curved boundaries show good agreement with both linear finite element simulations and experiments.

Elastic multipole method for describing deformation of infinite two-dimensional solids with circular inclusions.

Elastic materials with holes and inclusions are important in a large variety of contexts ranging from construction material to biological membranes. More recently, they have also been exploited in mechanical metamaterials, where the geometry of highly deformable structures is responsible for their unusual properties, such as negative Poisson's ratio, mechanical cloaking, and tunable phononic band gaps. Understanding how such structures deform in response to applied external loads is thus crucial for designing novel mechanical metamaterials. Here we present a method for predicting the linear response of infinite 2D solid structures with circular holes and inclusions by employing analogies with electrostatics. Just like an external electric field induces polarization (dipoles, quadrupoles, and other multipoles) of conductive and dielectric objects, external stress induces elastic multipoles inside holes and inclusions. Stresses generated by these induced elastic multipoles then lead to interactions between holes and inclusions, which induce additional polarization and thus additional deformation of holes and inclusions. We present a method that expands the induced polarization in a series of elastic multipoles, which systematically takes into account the interactions of inclusions and holes with the external stress field and also between them. The results of our method show good agreement with both linear finite element simulations and experiments.

Local accumulation of extracellular matrix regulates global morphogenetic patterning in the developing mammary gland.

The tree-like pattern of the mammary epithelium is formed during puberty through a process known as branching morphogenesis. Although mammary epithelial branching is stochastic and generates an epithelial tree with a random pattern of branches, the global orientation of the developing epithelium is predictably biased along the long axis of the gland. Here, we combine analysis of pubertal mouse mammary glands, a three-dimensional (3D)-printed engineered tissue model, and computational models of morphogenesis to investigate the origin and the dynamics of the global bias in epithelial orientation during pubertal mammary development. Confocal microscopy analysis revealed that a global bias emerges in the absence of pre-aligned networks of type I collagen in the fat pad and is maintained throughout pubertal development until the widespread formation of lateral branches. Using branching and annihilating random walk simulations, we found that the angle of bifurcation of terminal end buds (TEBs) dictates both the dynamics and the extent of the global bias in epithelial orientation. Our experimental and computational data demonstrate that a local increase in stiffness from the accumulation of extracellular matrix, which constrains the angle of bifurcation of TEBs, is sufficient to pattern the global orientation of the developing mammary epithelium. These data reveal that local mechanical properties regulate the global pattern of mammary epithelial branching and may provide new insight into the global patterning of other branched epithelia.

Clonal dominance in excitable cell networks.

Clonal dominance arises when the descendants (clones) of one or a few founder cells contribute disproportionally to the final structure during collective growth [1-8]. In contexts such as bacterial growth, tumorigenesis, and stem cell reprogramming [2-4], this phenomenon is often attributed to pre-existing propensities for dominance, while in stem cell homeostasis, neutral drift dynamics are invoked [5,6]. The mechanistic origin of clonal dominance during development, where it is increasingly documented [1,6-8], is less understood. Here, we investigate this phenomenon in the Drosophila melanogaster follicle epithelium, a system in which the joint growth dynamics of cell lineage trees can be reconstructed. We demonstrate that clonal dominance can emerge spontaneously, in the absence of pre-existing biases, as a collective property of evolving excitable networks through coupling of divisions among connected cells. Similar mechanisms have been identified in forest fires and evolving opinion networks [9-11]; we show that the spatial coupling of excitable units explains a critical feature of the development of the organism, with implications for tissue organization and dynamics [1,12,13].

Designing the Morphology of Separated Phases in Multicomponent Liquid Mixtures.

Phase separation of multicomponent liquid mixtures plays an integral part in many processes ranging from industry to cellular biology. In many cases the morphology of coexisting phases is crucially linked to the function of the separated mixture, yet it is unclear what determines the morphology when multiple phases are present. We developed a graph theory approach to predict the topology of coexisting phases from a given set of surface energies, enumerate all topologically distinct morphologies, and reverse engineer conditions for surface energies that produce the target morphology.

Size-dependent patterns of cell proliferation and migration in freely-expanding epithelia.

The coordination of cell proliferation and migration in growing tissues is crucial in development and regeneration but remains poorly understood. Here, we find that, while expanding with an edge speed independent of initial conditions, millimeter-scale epithelial monolayers exhibit internal patterns of proliferation and migration that depend not on the current but on the initial tissue size, indicating memory effects. Specifically, the core of large tissues becomes very dense, almost quiescent, and ceases cell-cycle progression. In contrast, initially-smaller tissues develop a local minimum of cell density and a tissue-spanning vortex. To explain vortex formation, we propose an active polar fluid model with a feedback between cell polarization and tissue flow. Taken together, our findings suggest that expanding epithelia decouple their internal and edge regions, which enables robust expansion dynamics despite the presence of size- and history-dependent patterns in the tissue interior.

Cells do not exist in isolation. Instead, they form tissues, where individual cells make contact with their neighbors and form microscopic 'architectures'. Epithelia are a type of tissue where cells are arranged in flat sheets, and are found in organs such as the lining of the kidney or the skin. Tissues need to grow, especially early in life. If tissues are damaged ­ for example, if the skin is cut or grazed ­ cells also need to divide (to create new healthy cells) and move as a group (to close the wound). Such coordinated motions result in cells exhibiting distinct group behaviors, similar to those observed within crowds of people or schools of fish. If coordination breaks down, problems can happen such as uncoordinated tissue growth seen in cancer. However, how cell movements are coordinated is still not fully understand. For example, researchers know that cells' positions within a group can determine how they behave, meaning that even the same type of cell could behave differently at the edge or center of a tissue. This suggests that the initial size and shape of a tissue should influence its subsequent growth and behavior; however, the nature of this influence is still largely unknown. Heinrich et al. therefore wanted to determine the differences in the way larger and smaller tissues grow. Microscope imaging was used to track the growth of circular, artificial tissues made from single-layered sheets of dog kidney cells grown in the laboratory. Comparing how quickly the tissues expanded revealed that the area of tissue circles that started out smaller increased at a much faster rate than that of tissue circles that were larger to begin with. This turned out to be because the edges of the tissues grew at a constant speed, independent of their initial size or shape, but circles with a smaller area have a larger proportion of cells on their edges. The motions of the cells at the center of the tissues had no effect on how the edges of the tissue grew. A final observation was that the way tissues of a given size behaved depended on whether they had grown to be that size, or they started off that big. These results shed light on how groups of cells interact in growing tissues. In the future, this information could be used to predict how different tissues grow over time, potentially helping scientists engineer better artificial tissues or organs for transplantation.

Finite Temperature Phase Behavior of Viral Capsids as Oriented Particle Shells.

A general phase plot is proposed for discrete particle shells that allows for thermal fluctuations of the shell geometry and of the inter-particle connectivities. The phase plot contains a first-order melting transition, a buckling transition, and a collapse transition and is used to interpret the thermodynamics of microbiological shells.

Nonuniform growth and surface friction determine bacterial biofilm morphology on soft substrates.

During development, organisms acquire three-dimensional (3D) shapes with important physiological consequences. While basic mechanisms underlying morphogenesis are known in eukaryotes, it is often difficult to manipulate them in vivo. To circumvent this issue, here we present a study of developing Vibrio cholerae biofilms grown on agar substrates in which the spatiotemporal morphological patterns were altered by varying the agar concentration. Expanding biofilms are initially flat but later undergo a mechanical instability and become wrinkled. To gain mechanistic insights into this dynamic pattern-formation process, we developed a model that considers diffusion of nutrients and their uptake by bacteria, bacterial growth/biofilm matrix production, mechanical deformation of both the biofilm and the substrate, and the friction between them. Our model shows quantitative agreement with experimental measurements of biofilm expansion dynamics, and it accurately predicts two distinct spatiotemporal patterns observed in the experiments-the wrinkles initially appear either in the peripheral region and propagate inward (soft substrate/low friction) or in the central region and propagate outward (stiff substrate/high friction). Our results, which establish that nonuniform growth and friction are fundamental determinants of stress anisotropy and hence biofilm morphology, are broadly applicable to bacterial biofilms with similar morphologies and also provide insight into how other bacterial biofilms form distinct wrinkle patterns. We discuss the implications of forming undulated biofilm morphologies, which may enhance the availability of nutrients and signaling molecules and serve as a "bet hedging" strategy.

Smooth muscle differentiation shapes domain branches during mouse lung development.

During branching morphogenesis, a simple cluster of cells proliferates and branches to generate an arborized network that facilitates fluid flow. The overall architecture of the mouse lung is established by domain branching, wherein new branches form laterally off the side of an existing branch. The airway epithelium develops concomitantly with a layer of smooth muscle that is derived from the embryonic mesenchyme. Here, we examined the role of smooth muscle differentiation in shaping emerging domain branches. We found that the position and morphology of domain branches are highly stereotyped, as is the pattern of smooth muscle that differentiates around the base of each branch. Perturbing the pattern of smooth muscle differentiation genetically or pharmacologically causes abnormal domain branching. Loss of smooth muscle results in ectopic branching and decreases branch stereotypy. Increased smooth muscle suppresses branch initiation and extension. Computational modeling revealed that epithelial proliferation is insufficient to generate domain branches and that smooth muscle wrapping is required to shape the epithelium into a branch. Our work sheds light on the physical mechanisms of branching morphogenesis in the mouse lung.