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Cell Division and Motility Enable Hexatic Order in Biological Tissues

Biological tissues transform between solid-like and liquid-like 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. 

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Discontinuous shear thickening in biological tissue rheology

Embryonic morphogenesis is characterized by significant tissue deformations, essential for shaping functional organs. Analogously, tissues in adult organisms persistently confront and adapt to mechanical forces and deformations, a testament to the critical role of cellular resilience and collective fluidity in developmental success and physiological maintenance. These transformations are often influenced by mechanical disturbances that stem from cellular activity, which can counter or coincide with the external stresses from surrounding tissues and organs. Traditionally, research into tissue mechanics has focused on responses to either external or internal forces, rarely addressing their interplay.

In our study, we leverage an active vertex model of 2D confluent tissue to probe the intricate dynamics between global external deformations and local internal active stresses generated by cell motility. We particularly spotlight how this dynamic tension governs the tissue's emergent mechanical characteristics. Approaching a solid-fluid jamming/unjamming transition, our model reveals an array of intriguing rheological behaviors, such as yielding, shear thinning, and both continuous and discontinuous shear thickening. These insights offer a theoretical foundation for interpreting the complex nonlinear rheological behavior observed in living tissues.

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Bridging the Gap Between Collective Motility and Epithelial-Mesenchymal Transitions through the Active Finite Voronoi Model

We have developed an active variant of the recently proposed finite Voronoi model for epithelial tissues. The Active Finite Voronoi (AFV) model facilitates the exploration of both confluent and non-confluent tissue geometries, as well as the transitions between them, in the context of active cellular dynamics. Our research uncovers a comprehensive phase diagram that bridges the process leading to collective cell motility through unjamming with the motility phenomena induced by the epithelial-mesenchymal transition (EMT). This model is poised to offer significant insights into critical problems in developmental biology and during the progression of cancer metastasis.

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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.

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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 fluid-like 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 solid-like 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.

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Glassy Behavior, Intermittency, and Cell Streaming in Epithelial Tissues

Embryonic development, tissue repair, and cancer progression all rely on neighboring cells rearranging themselves in biological tissue. One basic unit of such movement of cells in close-packed tissues is the T1 transition, where two cells swap positions. Because of the time required to remodel complex structures at junctions between cells, T1 transition cannot occur instantaneously. How this biological constraint affects collective behaviors among cells inside tissues is not known. Using theoretical modeling and simulations, we demonstrate that cell-level control of the time it takes to complete a T1 transition has unique consequences that change the ways cells mechanically interact, collectively organize, and migrate.

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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.

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Unjamming transition vs. the Epithelial-to-Mesenchymal transition in epithelial tissues

The epithelial-to-mesenchymal transition (EMT) and the unjamming transition (UJT) each comprises a gateway to cellular migration, plasticity and remodeling, but the extent to which these core programs are distinct, overlapping, or identical has remained undefined. Here, we triggered partial EMT (pEMT) or UJT in differentiated primary human bronchial epithelial cells. After triggering UJT, cell-cell junctions, apico-basal polarity, and barrier function remain intact, cells elongate and align into cooperative migratory packs, and mesenchymal markers of EMT remain unapparent. After triggering pEMT these and other metrics of UJT versus pEMT diverge. A computational model attributes effects of pEMT mainly to diminished junctional tension but attributes those of UJT mainly to augmented cellular propulsion. Through the actions of UJT and pEMT working independently, sequentially, or interactively, those tissues that are subject to development, injury, or disease become endowed with rich mechanisms for cellular migration, plasticity, self-repair, and regeneration.

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Effect of phenotypic heterogeneity in epithelial layers

Heterogeneity amongst cells in a tumor has been recognized as one of the hallmarks of cancer. This so-called intratumor heterogeneity is thought to facilitate metastasis by allowing a cellular community the flexibility and efficiency to adapt to new environments. It is also largely responsible for therapeutic resistance. Cellular differences within a tumor result from an interplay of both genetic and extrinsic influences. Whereas fitness or genotypic heterogeneity has been studied extensively, the role of mechanical heterogeneity in a tumor or cellular collective is still not well understood.

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Understanding the Origin of Mechanical Rigidity in Biological Tissues

Every organ in the human body is lined with epithelial cells. The cells in these tissues are normally sedentary or solid-like but become migratory or fluid-like during embryonic development, tissue repair, and cancer invasion. Researchers do not understand this striking transition from stationary to active behaviors, which could help shed light on various aspects of biology, medicine, and disease progression. We develop a theoretical model of cellular organization in these tissues that takes into account more complex junctions between cells than previous models—junctions that provide insight into this stark difference in cell behavior.

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Disordered Photonic Materials 

We design an amorphous material with a full photonic bandgap inspired by how cells pack in biological tissues. The size of the photonic bandgap can be manipulated through thermal and mechanical tuning. These directionally isotropic photonic bandgaps persist in solid and fluid phases, hence giving rise to a photonic fluid-like state that is robust with respect to fluid flow, rearrangements, and thermal fluctuations in contrast to traditional photonic crystals. This design should lead to the engineering of self-assembled nonrigid photonic structures with photonic bandgaps that can be controlled in real time via mechanical and thermal tuning.

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Mechnosensing and Mechanotransduction during wound healing

Many developmental processes involve collective cell motion, driven by migratory behaviors of individual cells and their interactions with the extracellular environment. An outstanding question is how cells regulate their internal driving forces to maintain tissue cohesiveness while promoting the requisite fluidity for collective motion. Progress has been limited by the lack of an integrative framework that couples cellular physical behavior with stochastic biochemical dynamics underlying cell motion and adhesion. Here we develop a cell-based computational model for collective cell migration during epithelial wound repair that integrates tissue mechanics with active cell motility, cell-substrate adhesions, and actomyosin dynamics. Using this model we show that an optimum balance of protrusive cell crawling and actomyosin contractility drives rapid directed motion of cohesive cell groups, robust to variations in cell and substrate physical properties. We further show that disparate modes of individual cell migration can cooperate to accelerate collective cell migration by fluidizing confluent tissues.

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