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.

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.

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.

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.

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.

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.

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.

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.

Spontaneous formation of aligned DNA nanowires by capillarity-induced skin folding.

Although DNA nanowires have proven useful as a template for fabricating functional nanomaterials and a platform for genetic analysis, their widespread use is still hindered because of limited control over the size, geometry, and alignment of the nanowires. Here, we document the capillarity-induced folding of an initially wrinkled surface and present an approach to the spontaneous formation of aligned DNA nanowires using a template whose surface morphology dynamically changes in response to liquid. In particular, we exploit the familiar wrinkling phenomenon that results from compression of a thin skin on a soft substrate. Once a droplet of liquid solution containing DNA molecules is placed on the wrinkled surface, the liquid from the droplet enters certain wrinkled channels. The capillary forces deform wrinkles containing liquid into sharp folds, whereas the neighboring empty wrinkles are stretched out. In this way, we obtain a periodic array of folded channels that contain liquid solution with DNA molecules. Such an approach serves as a template for the fabrication of arrays of straight or wrinkled DNA nanowires, where their characteristic scales are robustly tunable with the physical properties of liquid and the mechanical and geometrical properties of the elastic system.

Phase behavior and morphology of multicomponent liquid mixtures.

Multicomponent systems are ubiquitous in nature and industry. While the physics of few-component liquid mixtures (i.e., binary and ternary ones) is well-understood and routinely taught in undergraduate courses, the thermodynamic and kinetic properties of N-component mixtures with N > 3 have remained relatively unexplored. An example of such a mixture is provided by the intracellular fluid, in which protein-rich droplets phase separate into distinct membraneless organelles. In this work, we investigate equilibrium phase behavior and morphology of N-component liquid mixtures within the Flory-Huggins theory of regular solutions. In order to determine the number of coexisting phases and their compositions, we developed a new algorithm for constructing complete phase diagrams, based on numerical convexification of the discretized free energy landscape. Together with a Cahn-Hilliard approach for kinetics, we employ this method to study mixtures with N = 4 and 5 components. We report on both the coarsening behavior of such systems, as well as the resulting morphologies in three spatial dimensions. We discuss how the number of coexisting phases and their compositions can be extracted with Principal Component Analysis (PCA) and K-means clustering algorithms. Finally, we discuss how one can reverse engineer the interaction parameters and volume fractions of components in order to achieve a range of desired packing structures, such as nested "Russian dolls" and encapsulated Janus droplets.

Effects of thymic selection of the T-cell repertoire on HLA class I-associated control of HIV infection.

Without therapy, most people infected with human immunodeficiency virus (HIV) ultimately progress to AIDS. Rare individuals ('elite controllers') maintain very low levels of HIV RNA without therapy, thereby making disease progression and transmission unlikely. Certain HLA class I alleles are markedly enriched in elite controllers, with the highest association observed for HLA-B57 (ref. 1). Because HLA molecules present viral peptides that activate CD8(+) T cells, an immune-mediated mechanism is probably responsible for superior control of HIV. Here we describe how the peptide-binding characteristics of HLA-B57 molecules affect thymic development such that, compared to other HLA-restricted T cells, a larger fraction of the naive repertoire of B57-restricted clones recognizes a viral epitope, and these T cells are more cross-reactive to mutants of targeted epitopes. Our calculations predict that such a T-cell repertoire imposes strong immune pressure on immunodominant HIV epitopes and emergent mutants, thereby promoting efficient control of the virus. Supporting these predictions, in a large cohort of HLA-typed individuals, our experiments show that the relative ability of HLA-B alleles to control HIV correlates with their peptide-binding characteristics that affect thymic development. Our results provide a conceptual framework that unifies diverse empirical observations, and have implications for vaccination strategies.

Complex ordered patterns in mechanical instability induced geometrically frustrated triangular cellular structures.

Geometrical frustration arises when a local order cannot propagate throughout the space because of geometrical constraints. This phenomenon plays a major role in many systems leading to disordered ground-state configurations. Here, we report a theoretical and experimental study on the behavior of buckling-induced geometrically frustrated triangular cellular structures. To our surprise, we find that buckling induces complex ordered patterns which can be tuned by controlling the porosity of the structures. Our analysis reveals that the connected geometry of the cellular structure plays a crucial role in the generation of ordered states in this frustrated system.

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.

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.

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.

Statistical mechanical concepts in immunology.

Higher organisms, such as humans, have an adaptive immune system that usually enables them to successfully combat diverse (and evolving) microbial pathogens. The adaptive immune system is not preprogrammed to respond to prescribed pathogens. Yet it mounts pathogen-specific responses against diverse microbes and establishes memory of past infections (the basis of vaccination). Although major advances have been made in understanding pertinent molecular and cellular phenomena, the mechanistic principles that govern many aspects of an immune response are not known. We illustrate how complementary approaches from the physical and life sciences can help confront this challenge. Specifically, we describe work that brings together statistical mechanics and cell biology to shed light on how key molecular/cellular components of the adaptive immune system are selected to enable pathogen-specific responses. We hope these examples encourage physical chemists to work at this crossroad of disciplines where fundamental discoveries with implications for human health might be made.

How the thymus designs antigen-specific and self-tolerant T cell receptor sequences.

T lymphocytes (T cells) orchestrate adaptive immune responses that clear pathogens from infected hosts. T cells recognize short peptides (p) derived from antigenic proteins bound to protein products of the MHC genes. Recognition occurs when T cell receptor (TCR) proteins expressed on T cells bind sufficiently strongly to antigen-derived pMHC complexes on the surface of antigen-presenting cells. A diverse repertoire of self-pMHC-tolerant TCR sequences is shaped during development of T cells in the thymus by processes called positive and negative selection. Combining computational models and analysis of experimental data, we parsed the contributions of positive and negative selection to the design of TCR sequences that recognize antigenic peptides with specificity, yet also exhibit cross-reactivity. A dominant role for negative selection in mediating antigen specificity of mature T cells and a molecular mechanism for TCR recognition of antigen are described.

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.