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My approach to solve a research problem
Define the question, Develop the theory, Simulate to get deeper insights, and Match with existing or new experiments for Validation.
Dynamics and statics of confluent cell monolayers
Our research develops a unified physical framework connecting cell shape, shape variability, and collective dynamics in confluent tissues. Epithelial cell monolayers often undergo solid-to-fluid-like transitions during several biological processes such as embryogenesis, cancer progression, asthma advancement, wound healing, and vertebrate body elongation. Cell shape and dynamics change a lot during these processes. For the last few decades, experiments on confluent cell monolayers have reported that this solid-to-fluid-like transition shows remarkable similarities with glassy dynamics; it exhibits slow relaxation, dynamical heterogeneity, non-Gaussian motion, etc. We extend theories from condensed-matter physics, including random first-order transition theory (RFOT) and mode-coupling theory (MCT), to cellular systems and test their predictions using computational models such as the cellular Potts models, Vertex models, and the Voronoi model. Altering the control parameter of dynamics, i.e., P0, governs the tissue relaxation dynamics and switches the relaxation mechanism from super-Arrhenius to sub-Arrhenius. We showed that the structure-dynamics feedback mechanism of MCT works better in the sub-Arrhenius regime, whereas the barrier-crossing mechanism of RFOT explains the super-Arrhenius regime well. At the same time, we investigate how cell shape and cell-to-cell variability reflect the underlying mechanical and dynamical state of the tissue. Rather than treating shape fluctuations as biological noise, we develop mean-field theories that connect aspect-ratio distributions to the underlying energy landscape of confluent systems. These theories predict near-universal distributions of scaled cell shape and a universal relationship between mean shape and shape variability across diverse epithelial tissues, cancer cell lines, developmental systems, and computational models. We found that the distribution of cell shape is described by a single parameter (alpha) that includes all system-specific details. Our results imply that in a confluent monolayer, cell shape variability is inevitable, where a single parameter describes both statics and dynamics. We have also connected dynamical heterogeneity with this universal mean cell shape and cell-to-cell shape variability relation. Together, these efforts aim to establish cell shape as a quantitative bridge between tissue mechanics, glassy dynamics, and biological function in development, disease, and collective cell migration.
Active Matter: Physics of living organisms
Activity is a part and parcel of our life. Living materials, including cytoskeletal networks, bacterial colonies, and confluent epithelial monolayers, are composed of complex units that continuously consume energy and drive the system away from thermal equilibrium. Energy injection at the scale of molecular motors or individual cells, together with mechanical, biochemical, and collective interactions, can produce emergent behaviors such as flocking, directed migration, phase separation, unjamming, and glass-like dynamical arrest. Our research aims to identify the physical design principles that connect microscopic active processes to these large-scale structural and dynamical properties. Building on our random first-order transition theory for passive confluent tissues, we have now developed a unified theoretical framework for active cell monolayers. Two crucial aspects of epithelial cellular systems, confluency and self-propulsion, have been theoretically studied in separate works. Here we include both these aspects within a single framework and study their combined effects on the glassy properties. One crucial result of this work is that confluency modifies the self-propulsion. This modification comes through an effective rotational diffusivity, Dr^{eff}. We showed that Dr^{eff} is proportional to Dr when Dr is small, and saturates at higher values of Dr via some phenomenological argument. The origin of this modification is the cell-cell friction at the boundary of the cells, which hinders the free rotation of the cells. This modified self-propulsion enters the extension of the RFOT theory. Our predictions are in good agreement with existing data on the Voronoi model and new simulations on the active Vertex model.
Learning from biological data of cells from different organisms
Mechanical properties of the cells
Fluctuation-dominated phase ordering
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