Discontinuous Shear Thickening in Biological Tissue Rheology.

During embryonic morphogenesis, tissues undergo dramatic deformations in order to form functional organs. Similarly, in adult animals, living cells and tissues are continually subjected to forces and deformations. Therefore, the success of embryonic development and the proper maintenance of physiological functions rely on the ability of cells to withstand mechanical stresses as well as their ability to flow in a collective manner. During these events, mechanical perturbations can originate from active processes at the single-cell level, competing with external stresses exerted by surrounding tissues and organs. However, the study of tissue mechanics has been somewhat limited to either the response to external forces or to intrinsic ones. In this work, we use an active vertex model of a 2D confluent tissue to study the interplay of external deformations that are applied globally to a tissue with internal active stresses that arise locally at the cellular level due to cell motility. We elucidate, in particular, the way in which this interplay between globally external and locally internal active driving determines the emergent mechanical properties of the tissue as a whole. For a tissue in the vicinity of a solid-fluid jamming or unjamming transition, we uncover a host of fascinating rheological phenomena, including yielding, shear thinning, continuous shear thickening, and discontinuous shear thickening. These model predictions provide a framework for understanding the recently observed nonlinear rheological behaviors in vivo.

A shape-driven reentrant jamming transition in confluent monolayers of synthetic cell-mimics.

Many critical biological processes, like wound healing, require densely packed cell monolayers/tissues to transition from a jammed solid-like to a fluid-like state. Although numerical studies anticipate changes in the cell shape alone can lead to unjamming, experimental support for this prediction is not definitive because, in living systems, fluidization due to density changes cannot be ruled out. Additionally, a cell's ability to modulate its motility only compounds difficulties since even in assemblies of rigid active particles, changing the nature of self-propulsion has non-trivial effects on the dynamics. Here, we design and assemble a monolayer of synthetic cell-mimics and examine their collective behaviour. By systematically increasing the persistence time of self-propulsion, we discovered a cell shape-driven, density-independent, re-entrant jamming transition. Notably, we observed cell shape and shape variability were mutually constrained in the confluent limit and followed the same universal scaling as that observed in confluent epithelia. Dynamical heterogeneities, however, did not conform to this scaling, with the fast cells showing suppressed shape variability, which our simulations revealed is due to a transient confinement effect of these cells by their slower neighbors. Our experiments unequivocally establish a morphodynamic link, demonstrating that geometric constraints alone can dictate epithelial jamming/unjamming.

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions.

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

Cell Division and Motility Enable Hexatic Order in Biological Tissues.

Biological tissues transform between solid- and liquidlike states in many fundamental physiological events. Recent experimental observations further suggest that in two-dimensional epithelial tissues these solid-liquid transformations can happen via intermediate states akin to the intermediate hexatic phases observed in equilibrium two-dimensional melting. The hexatic phase is characterized by quasi-long-range (power-law) orientational order but no translational order, thus endowing some structure to an otherwise structureless fluid. While it has been shown that hexatic order in tissue models can be induced by motility and thermal fluctuations, the role of cell division and apoptosis (birth and death) has remained poorly understood, despite its fundamental biological role. Here we study the effect of cell division and apoptosis on global hexatic order within the framework of the self-propelled Voronoi model of tissue. Although cell division naively destroys order and active motility facilitates deformations, we show that their combined action drives a liquid-hexatic-liquid transformation as the motility increases. The hexatic phase is accessed by the delicate balance of dislocation defect generation from cell division and the active binding of disclination-antidisclination pairs from motility. We formulate a mean-field model to elucidate this competition between cell division and motility and the consequent development of hexatic order.

Regulation of Chromatin Modifications through Coordination of Nucleus Size and Epithelial Cell Morphology Heterogeneity.

Cell morphology heterogeneity within epithelial collectives is a pervasive phenomenon intertwined with tissue mechanical properties. Despite its widespread occurrence, the underlying mechanisms driving cell morphology heterogeneity and its consequential biological ramifications remain elusive. Here, we investigate the dynamic evolution of epithelial cell morphology and nucleus morphology during crowding, unveiling a consistent correlation between the two. Our investigation reveals a persistent log-normal probability distribution characterizing both cell and nucleus areas across diverse crowding stages and epithelial model systems. We showed that this morphological diversity arises from asymmetric partitioning during cell division and is perpetuated through actomyosin-mediated regulation of cell-nucleus size coordination. Moreover, we provide insights into the impact of nucleus morphology on chromatin dynamics, demonstrating that constraining nucleus area leads to downregulation of the euchromatic mark H3K9ac and upregulation of the heterochromatic mark H3K27me3 through modulation of histone demethylase UTX expression. These findings under-score the significance of cell morphology heterogeneity as a driver of chromatin state diversity, shaping functional variability within epithelial tissues.

Spatial confinement affects the heterogeneity and interactions between shoaling fish.

Living objects are able to consume chemical energy and process information independently from others. However, living objects can coordinate to form ordered groups such as schools of fish. This work considers these complex groups as living materials and presents imaging-based experiments of laboratory schools of fish to understand how activity, which is a non-equilibrium feature, affects the structure and dynamics of a group. We use spatial confinement to control the motion and structure of fish within quasi-2D shoals of fish and use image analysis techniques to make quantitative observations of the structures, their spatial heterogeneity, and their temporal fluctuations. Furthermore, we utilize Monte Carlo simulations to replicate the experimentally observed data which provides insight into the effective interactions between fish and confirms the presence of a confinement-based behavioral preference transition. In addition, unlike in short-range interacting systems, here structural heterogeneity and dynamic activities are positively correlated as a result of complex interplay between spatial arrangement and behavioral dynamics in fish collectives.

Nuclear size-regulated emergence of topological packing order on growing human lung alveolospheres.

Within multicellular living systems, cells coordinate their positions with spatiotemporal accuracy to form various structures, setting the clock to control developmental processes and trigger maturation. These arrangements can be regulated by tissue topology, biochemical cues, as well as mechanical perturbations. However, the fundamental rules of how local cell packing order is regulated in forming three-dimensional (3D) multicellular architectures remain unclear. Furthermore, how cellular coordination evolves during developmental processes, and whether this cell patterning behavior is indicative of more complex biological functions, is largely unknown. Here, using human lung alveolospheres as a model system, by combining experiments and numerical simulations, we find that, surprisingly, cell packing behavior on alveolospheres resembles hard-disk packing but with increased randomness; the stiffer cell nuclei act as the hard disks surrounded by deformable cell bodies. Interestingly, we observe the emergence of topological packing order during alveolosphere growth, as a result of increasing nucleus-to-cell size ratio. Specifically, we find more hexagon-concentrated cellular packing with increasing bond orientational order, indicating a topological gas-to-liquid transition. Additionally, by osmotically changing the compactness of cells on alveolospheres, we observe that the variations in packing order align with the change of nucleus-to-cell size ratio. Together, our findings reveal the underlying rules of cell coordination and topological phases during human lung alveolosphere growth. These static packing characteristics are consistent with cell dynamics, together suggesting that better cellular packing stabilizes local cell neighborhoods and may regulate more complex biological functions such as organ development and cellular maturation.

Matrix confinement modulates 3D spheroid sorting and burst-like collective migration.

While it is known that cells with differential adhesion tend to segregate and preferentially sort, the physical forces governing sorting and invasion in heterogeneous tumors remain poorly understood. To investigate this, we tune matrix confinement, mimicking changes in the stiffness and confinement of the tumor microenvironment, to explore how physical confinement influences individual and collective cell migration in 3D spheroids. High levels of confinement lead to cell sorting while reducing matrix confinement triggers the collective fluidization of cell motion. Cell sorting, which depends on cell-cell adhesion, is crucial to this phenomenon. Burst-like migration does not occur for spheroids that have not undergone sorting, regardless of the degree of matrix confinement. Using computational Self-Propelled Voronoi modeling, we show that spheroid sorting and invasion into the matrix depend on the balance between cell-generated forces and matrix resistance. The findings support a model where matrix confinement modulates 3D spheroid sorting and unjamming in an adhesion-dependent manner, providing insights into the mechanisms of cell sorting and migration in the primary tumor and toward distant metastatic sites. STATEMENT OF SIGNIFICANCE: The mechanical properties of the tumor microenvironment significantly influence cancer cell migration within the primary tumor, yet how these properties affect intercellular interactions in heterogeneous tumors is not well understood. By utilizing calcium and calcium chelators, we dynamically alter collagen-alginate hydrogel stiffness and investigate tumor cell behavior within co-culture spheroids in response to varying degrees of matrix confinement. High confinement is found to trigger cell sorting while reducing confinement for sorted spheroids facilitates collective cell invasion. Notably, without prior sorting, spheroids do not exhibit burst-like migration, regardless of confinement levels. This work establishes that matrix confinement and intercellular adhesion regulate 3D spheroid dynamics, offering insights into cellular organization and migration within the primary tumor.

Effect of non-linear strain stiffening in eDAH and unjamming.

In cell clusters, the prominent factors at play encompass contractility-based enhanced tissue surface tension and cell unjamming transition. The former effect pertains to the boundary effect, while the latter constitutes a bulk effect. Both effects share outcomes of inducing significant elongation in cells. This elongation is so substantial that it surpasses the limits of linear elasticity, thereby giving rise to additional effects. To investigate these effects, we employ atomic force microscopy (AFM) to analyze how the mechanical properties of individual cells change under such considerable elongation. Our selection of cell lines includes MCF-10A, chosen for its pronounced demonstration of the extended differential adhesion hypothesis (eDAH), and MDA-MB-436, selected due to its manifestation of cell unjamming behavior. In the AFM analyses, we observe a common trend in both cases: as elongation increases, both cell lines exhibit strain stiffening. Notably, this effect is more prominent in MCF-10A compared to MDA-MB-436. Subsequently, we employ AFM on a dynamic range of 1-200 Hz to probe the mechanical characteristics of cell spheroids, focusing on both surface and bulk mechanics. Our findings align with the results from single cell investigations. Specifically, MCF-10A cells, characterized by strong contractile tissue tension, exhibit the greatest stiffness on their surface. Conversely, MDA-MB-436 cells, which experience significant elongation, showcase their highest stiffness within the bulk region. Consequently, the concept of single cell strain stiffening emerges as a crucial element in understanding the mechanics of multicellular spheroids (MCSs), even in the case of MDA-MB-436 cells, which are comparatively softer in nature.

Network physics of attractive colloidal gels: Resilience, rigidity, and phase diagram.

Colloidal gels exhibit solid-like behavior at vanishingly small fractions of solids, owing to ramified space-spanning networks that form due to particle-particle interactions. These networks give the gel its rigidity, and with stronger attractions the elasticity grows as well. The emergence of rigidity can be described through a mean field approach; nonetheless, fundamental understanding of how rigidity varies in gels of different attractions is lacking. Moreover, recovering an accurate gelation phase diagram based on the system's variables has been an extremely challenging task. Understanding the nature of colloidal clusters, and how rigidity emerges from their connections is key to controlling and designing gels with desirable properties. Here, we employ network analysis tools to interrogate and characterize the colloidal structures. We construct a particle-level network, having all the spatial coordinates of colloids with different attraction levels, and also identify polydisperse rigid fractal clusters using a Gaussian mixture model, to form a coarse-grained cluster network that distinctly shows main physical features of the colloidal gels. A simple mass-spring model then is used to recover quantitatively the elasticity of colloidal gels from these cluster networks. Interrogating the resilience of these gel networks shows that the elasticity of a gel (a dynamic property) is directly correlated to its cluster network's resilience (a static measure). Finally, we use the resilience investigations to devise [and experimentally validate] a fully resolved phase diagram for colloidal gelation, with a clear solid-liquid phase boundary using a single volume fraction of particles well beyond this phase boundary.

Matrix confinement modulates 3D spheroid sorting and burst-like collective migration.

While it is known that cells with differential adhesion tend to segregate and preferentially sort, the physical forces governing sorting and invasion in heterogeneous tumors remain poorly understood. To investigate this, we tune matrix confinement, mimicking changes in the stiffness and confinement of the tumor microenvironment, to explore how physical confinement influences individual and collective cell migration in 3D spheroids. High levels of confinement lead to cell sorting while reducing matrix confinement triggers the collective fluidization of cell motion. Cell sorting, which depends on cell-cell adhesion, is crucial to this phenomenon. Burst-like migration does not occur for spheroids that have not undergone sorting, regardless of the degree of matrix confinement. Using computational Self-Propelled Voronoi modeling, we show that spheroid sorting and invasion into the matrix depend on the balance between cell-generated forces and matrix resistance. The findings support a model where matrix confinement modulates 3D spheroid sorting and unjamming in an adhesion-dependent manner, providing insights into the mechanisms of cell sorting and migration in the primary tumor and toward distant metastatic sites.

Mechanical imbalance between normal and cancer cells drives epithelial defense against cancer.

Cell competition enables normal wildtype cells of epithelial tissue to eliminate mutant cells expressing activated oncoproteins such as HRasV12. However, the driving force behind this fundamental epithelial defense against cancer remains enigmatic. Here, we employ tissue stress microscopy and theoretical modeling and invent a new collective compressibility measurement technique called gel compression microscopy to unveil the mechanism governing cell competition. Stress microscopy reveals unique compressive stress experienced by the mutant cells, contrasting with predominantly tensile stress experienced by normal cells. A cell-based computer simulation then predicts that this compressive stress arises out of a mechanical imbalance between two competing populations due to a difference in their collective compressibility and rigidity. Gel compression microscopy empirically confirms the prediction and elucidates a three-fold higher compressibility of the mutant population than the normal population. Mechanistically, this difference stems from the reduced abundance and coupling of junctional E-cadherin molecules in the mutant cells, which weakens cell-cell adhesions and renders the mutant population more compressible. Taken together, our study elucidates both the physical principle and the underlying molecular mechanism driving cell competition in epithelial defense against cancer and opens new directions for mechanomedicine in cancer.

Constitutive model for the rheology of biological tissue.

The rheology of biological tissue is key to processes such as embryo development, wound healing, and cancer metastasis. Vertex models of confluent tissue monolayers have uncovered a spontaneous liquid-solid transition tuned by cell shape; and a shear-induced solidification transition of an initially liquidlike tissue. Alongside this jamming/unjamming behavior, biological tissue also displays an inherent viscoelasticity, with a slow time and rate-dependent mechanics. With this motivation, we combine simulations and continuum theory to examine the rheology of the vertex model in nonlinear shear across a full range of shear rates from quastistatic to fast, elucidating its nonlinear stress-strain curves after the inception of shear of finite rate, and its steady state flow curves of stress as a function of strain rate. We formulate a rheological constitutive model that couples cell shape to flow and captures both the tissue solid-liquid transition and its rich linear and nonlinear rheology.

Nature-inspired designs for disordered acoustic bandgap materials.

We introduce an amorphous mechanical metamaterial inspired by how cells pack in biological tissues. The spatial heterogeneity in the local stiffness of these materials has been recently shown to impact the mechanics of confluent biological tissues and cancer tumor invasion. Here we use this bio-inspired structure as a design template to construct mechanical metamaterials and show that this heterogeneity can give rise to amorphous cellular solids with large, tunable acoustic bandgaps. Unlike acoustic crystals with periodic structures, the bandgaps here are directionally isotropic and robust to defects due to their complete lack of positional order. Possible ways to manipulate bandgaps are explored with a combination of the tissue-level elastic modulus and local stiffness heterogeneity of cells. To further demonstrate the existence of bandgaps, we dynamically perturb the system with an external sinusoidal wave in the perpendicular and horizontal directions. The transmission coefficients are calculated and show valleys that coincide with the location of bandgaps. Experimentally this design should lead to the engineering of self-assembled rigid acoustic structures with full bandgaps that can be controlled via mechanical tuning and promote applications in a broad area from vibration isolations to mechanical waveguides.

Discontinuous rigidity transition associated with shear jamming in granular simulations.

We investigate the rigidity transition associated with shear jamming in frictionless, as well as frictional, disk packings in the quasi-static regime and at low shear rates. For frictionless disks, the transition under quasi-static shear is discontinuous, with an instantaneous emergence of a system spanning rigid clusters at the jamming transition. For frictional systems, the transition appears continuous for finite shear rates, but becomes sharper for lower shear rates. In the quasi-static limit, it is discontinuous as in the frictionless case. Thus, our results show that the rigidity transition associated with shear jamming is discontinuous, as demonstrated in the past for isotropic jamming of frictionless particles, and therefore a unifying feature of the jamming transition in general.

Bridging the gap between collective motility and epithelial-mesenchymal transitions through the active finite voronoi model.

We introduce an active version of the recently proposed finite Voronoi model of epithelial tissue. The resultant Active Finite Voronoi (AFV) model enables the study of both confluent and non-confluent geometries and transitions between them, in the presence of active cells. Our study identifies six distinct phases, characterized by aggregation-segregation, dynamical jamming-unjamming, and epithelial-mesenchymal transitions (EMT), thereby extending the behavior beyond that observed in previously studied vertex-based models. The AFV model with rich phase diagram provides a cohesive framework that unifies the well-observed progression to collective motility via unjamming with the intricate dynamics enabled by EMT. This approach should prove useful for challenges in developmental biology systems as well as the complex context of cancer metastasis. The simulation code is also provided.

Epithelial layer fluidization by curvature-induced unjamming.

The transition of an epithelial layer from a stationary, quiescent state to a highly migratory, dynamic state is required for wound healing, development, and regeneration. This transition, known as the unjamming transition (UJT), is responsible for epithelial fluidization and collective migration. Previous theoretical models have primarily focused on the UJT in flat epithelial layers, neglecting the effects of strong surface curvature that is characteristic of epithelial tissues in vivo. In this study, we investigate the role of surface curvature on tissue plasticity and cellular migration using a vertex model embedded on a spherical surface. Our findings reveal that increasing curvature promotes epithelial unjamming by reducing the energy barriers to cellular rearrangements. Higher curvature favors cell intercalation, mobility, and self-diffusivity, resulting in epithelial structures that are malleable and migratory when small, but become more rigid and stationary as they grow. As such, curvature-induced unjamming emerges as a novel mechanism for epithelial layer fluidization. Our quantitative model proposes the existence of a new, extended, phase diagram wherein local cell shape, cell propulsion, and tissue geometry combine to determine the epithelial migratory phenotype.

Compressive stress drives adhesion-dependent unjamming transitions in breast cancer cell migration.

Cellular unjamming is the collective fluidization of cell motion and has been linked to many biological processes, including development, wound repair, and tumor growth. In tumor growth, the uncontrolled proliferation of cancer cells in a confined space generates mechanical compressive stress. However, because multiple cellular and molecular mechanisms may be operating simultaneously, the role of compressive stress in unjamming transitions during cancer progression remains unknown. Here, we investigate which mechanism dominates in a dense, mechanically stressed monolayer. We find that long-term mechanical compression triggers cell arrest in benign epithelial cells and enhances cancer cell migration in transitions correlated with cell shape, leading us to examine the contributions of cell-cell adhesion and substrate traction in unjamming transitions. We show that cadherin-mediated cell-cell adhesion regulates differential cellular responses to compressive stress and is an important driver of unjamming in stressed monolayers. Importantly, compressive stress does not induce the epithelial-mesenchymal transition in unjammed cells. Furthermore, traction force microscopy reveals the attenuation of traction stresses in compressed cells within the bulk monolayer regardless of cell type and motility. As traction within the bulk monolayer decreases with compressive pressure, cancer cells at the leading edge of the cell layer exhibit sustained traction under compression. Together, strengthened intercellular adhesion and attenuation of traction forces within the bulk cell sheet under compression lead to fluidization of the cell layer and may impact collective cell motion in tumor development and breast cancer progression.

Shear-Driven Solidification and Nonlinear Elasticity in Epithelial Tissues.

Biological processes, from morphogenesis to tumor invasion, spontaneously generate shear stresses inside living tissue. The mechanisms that govern the transmission of mechanical forces in epithelia and the collective response of the tissue to bulk shear deformations remain, however, poorly understood. Using a minimal cell-based computational model, we investigate the constitutive relation of confluent tissues under simple shear deformation. We show that an initially undeformed fluidlike tissue acquires finite rigidity above a critical applied strain. This is akin to the shear-driven rigidity observed in other soft matter systems. Interestingly, shear-driven rigidity can be understood by a critical scaling analysis in the vicinity of the second order critical point that governs the liquid-solid transition of the undeformed system. We further show that a solidlike tissue responds linearly only to small strains and but then switches to a nonlinear response at larger stains, with substantial stiffening. Finally, we propose a mean-field formulation for cells under shear that offers a simple physical explanation of shear-driven rigidity and nonlinear response in a tissue.

Configurational fingerprints of multicellular living systems.

Cells cooperate as groups to achieve structure and function at the tissue level, during which specific material characteristics emerge. Analogous to phase transitions in classical physics, transformations in the material characteristics of multicellular assemblies are essential for a variety of vital processes including morphogenesis, wound healing, and cancer. In this work, we develop configurational fingerprints of particulate and multicellular assemblies and extract volumetric and shear order parameters based on this fingerprint to quantify the system disorder. Theoretically, these two parameters form a complete and unique pair of signatures for the structural disorder of a multicellular system. The evolution of these two order parameters offers a robust and experimentally accessible way to map the phase transitions in expanding cell monolayers and during embryogenesis and invasion of epithelial spheroids.