Theoretical Soft Matter and Biophysics Group
Our research focuses on the non-equilibrium mechanics and collective behavior in biological systems and soft matter. One central theme is the investigation of the nature of solid-fluid transitions in amorphous systems, ranging from biological tissues and cancer tumors to colloids and granular materials. We use theoretical and numerical tools from biophysics, non-equilibrium statistical physics, condensed matter physics, and glassy physics to model and understand the complexity, patterns, and mechanical response that arise from the collective organizations of individual constituents (e.g., biological cells, grains, colloids).
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.
Yiwen Tang, Siyuan Chen, Mark J. Bowick, Dapeng Bi "Cell Division and Motility Enable Hexatic Order in Biological Tissues" (2023) https://arxiv.org/abs/2303.00129
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.
Margherita De Marzio, Amit Das, Jeffrey J. Fredberg, Dapeng Bi, "Epithelial layer fluidization by curvature-induced unjamming" (2023) https://arxiv.org/abs/2305.12667
Emergent modes of collective cell organization in an 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 results indicate a rich phase diagram which unifies the study of the route to collective motility via unjamming with the study of motility enabled by EMT, the epithelial-mesenchymal transition. This approach should prove useful for issues arising in both developmental biology systems and during cancer metastasis.
Junxiang Huang, Herbert Levine, Dapeng Bi "Emergent modes of collective cell organization in an Active Finite Voronoi model" (2023) https://arxiv.org/abs/2303.08276
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/unjamming transition, we uncover a host of fascinating rheological phenomena, including yielding, shear thinning, continuous shear thickening (CST) and discontinuous shear thickening (DST). These model predictions provide a framework for understanding the recently observed nonlinear rheological behaviors in vivo.
Michael J. Hertaeg, Suzanne M. Fielding, D. Bi "Discontinuous shear thickening in biological tissue rheology" (2023) https://arxiv.org/abs/2211.15015
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.
J. Huang et al “Stress-driven rigidity and non-linear elasticity in epithelial tissues.” (2021). Preprint: https://arxiv.org/abs/2109.10374
S. Fielding, J. Cochran, J. Huang, D. Bi, M. C. Marchetti, “Constitutive model for the rheology of biological tissue” (2023). https://arxiv.org/abs/2210.02893
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.
A. Das, S. Sastry & D. Bi. “Controlled neighbor exchanges drive glassy behavior, intermittency and cell streaming in epithelial tissues” Phys. Rev. X 11, 041037 (2021)
SZ Lin, WY Zhang, D. Bi, B Li, XQ Feng “Energetics of mesoscale cell turbulence in two-dimensional monolayers” Communications Physics 4 (1) (2021), 1-9
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.
H. Yang, A. F. Pegoraro, Y. Han, W. Tang, R. Abeyaratne, D. Bi, M. Guo. "Configurational fingerprints of multicellular living systems" PNAS (2021) , 118 (44) e2109168118
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.
J.A. Mitchel, A. Das, M. O’Sullivan, I. Stancil, S. DeCamp, S. Koehler, J.J. Fredberg, J. Drazen, J. P Butler, A. Nieto, D. Bi and J.-A. Park, “The unjamming transition is distinct from the epithelial-to-mesenchymal transition”, Nature Communications 11 5053 (2020)
J.-H. Kim et al “Unjamming and collective migration in MCF10A breast cancer cell lines." Biochemical and Biophysical Research Communications 521 3 (2020)
M. J. O'Sullivan, J. A. Mitchel, A. Das, S. Koehler, H. Levine, D. Bi., Z. D. Nagel, & J.-A Park. “Collective migration of non-cancerous, well-differentiated human airway epithelial cells by ionizing radiation", Frontiers in Cell and Developmental Biology 8 (2020)
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.
X. Li, A. Das, & D. Bi “Mechanical Heterogeneity in Tissues Promotes Rigidity and Controls Cellular Invasion", Physical Review Letters 123, 058101 (2019)
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.
L. Yan & D. Bi “Multicellular rosettes drive fluid-solid transition in epithelial tissues” Physical Review X 9 (011029) (2019)
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.
X. Li, A. Das, D. Bi "Biological tissue-inspired tunable photonic fluid" PNAS (2018), 115 (26) 6650-6655
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.
V. Ajeti et al, “Epithelial Wound Healing Coordinates Distinct F-actin Architectures to Conserve Work and Balance Power". Nature Physics 15, 696–705 (2019)
M. F. Staddon et al. “Cooperation of dual modes of cell motility promotes epithelial stress relaxation to accelerate wound healing” PLOS Computation Biology 14 (10) e1006502 (2018)