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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.
Below I will briefly summarize my research works.
Theoretical understanding of glassy dynamics in confluent cell monolayer
For the last few decades, experiments on confluent cell monolayers reported a solid-to-fluid-like transition that shows remarkable similarities with glassy dynamics. These confluent cell monolayers exhibit extreme slowing down of dynamics with a rapid increase in the relaxation time, complex two-step relaxation dynamics, dynamical heterogeneity, non-Gaussian displacement distribution etc. This striking similarity of confluent cell monolayer/tissues with glass opens up a biological realm of glassy dynamics of condensed matter physics. Despite these observations, there exists no proper theory of glassy dynamics for confluent epithelial cell monolayer. In this work, we have extended one of the popular theories of equilibrium glass for particulate systems, the Random first-order transition (RFOT) theory for confluent cellular systems. We validated our theoretical understanding via simulation on the cellular Potts model (CPM) of confluent tissues that uses an effective simple energy function to describe the dynamics of the cells in a tissue. We found that the target perimeter, P0, plays the role of a control parameter of dynamics. P0 parameterizes the interaction potential of the system. These confluent systems show unusual sub-Arrhenius relaxation, captured and verified by our theory and simulations. We have compared our simulation results on CPM with the existing experimental results which ensures the applicability of CPM to study the confluent cell monolayer in the glassy regime.
This work is published in Phys. Rev. E.
Non-trivial effect of activity on the glassy dynamics of confluent cell monolayer
As cancer progresses, cells in the confluent monolayers acquire in-plane polarity and perform persistent motion via epithelial-to-mesenchymal transition (EMT). During EMT, cells also exhibit solid-to-fluid-like glassy characteristics. However, the effect of activity on the glassy dynamics of the confluent cell monolayer remains unexplored. To understand the effects of different active processes at the cellular level on the approach to glass transition, we develop a general theoretical framework for active cell monolayer by extending the existing RFOT theory of passive cell monolayer developed by us. Two aspects of the 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 frictions 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.
This work is published in Soft Matter.
On the origin of universal cell shape variability of confluent cell monolayer
Change in cell shape is fundamental in several biological as well as pathological processes such as embryogenesis, cancer progression, asthma advancement, wound healing, and vertebrate body elongation. Cellular functions such as cell cycle events, division plane orientation, and neighbour exchange are often controlled by the cellular shape. For most of the experimental studies cellular functions are studied via the mean cell shape, characterized by the mean aspect ratio of the cells. However, cell-to-cell shape variability is mostly regarded as unimportant biological noise. However, in pioneer work, Atia et al. [Nat. Phys, 2018] have shown that cell shape and shape variability are mutually constrained through a purely geometrical relationship. They also reported that across the diverse epithelial monolayers, cell shape variability [scaled aspect ratio, rs is the ratio of (AR-1) to (average AR-1)] follows a nearly universal distribution. However, the origin and implications of this universality remain unclear. Therefore, in this work, we develop a mean-field theory for cell shape variability using the energy function of confluent cell monolayers. For the analytical calculation, we have made several simplifying assumptions, which are either motivated by experiments or justified in our simulations. We found that the distribution of cell shape is described by a single parameter 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. Our theoretical formula for the distribution of aspect ratio (r) agrees remarkably well with the simulation data of CPM, on the square and hexagonal lattices, and the VM. We have collected existing experimental and simulation data on different systems and show the PDFs of scaled aspect ratio, rs. The variety in our chosen set is spectacular: it consists of various cancer cell lines, both asthmatic and non-asthmatic HBEC cells, MDCK cells, Drosophila wing disk, simulations data on both active and equilibrium versions of the VM, the active Voronoi model, and the CPM. Yet, the PDFs look nearly universal and in agreement with our analytical theory. Our theory also predicts a strictly universal behaviour for sd (standard deviation of aspect ratio) vs. mean r which is independent of the system. Hence, it should be valid across diverse confluent monolayers. We have collected existing experimental data for several systems: cancerous cell lines, human breast cancer cells, and a jammed epithelial monolayer of MDCK cells. We showed that all the experimental data falls on our predicted theoretical line which ensures the diverse applicability of our theory.
This work is published in eLife.
Solid-to-fluid-like transition in dense epithelial cell tissues plays a crucial role in several developmental and pathological processes such as wound healing, embryogenesis, cancer metastasis, and asthma progression. In the solid-like jammed state, the cells are firmly connected and regularly shaped. On the other hand, they are elongated and move a lot in the fluid-like unjammed state. A biological tissue can be fluidized for many reasons such as uncontrolled rate of cell division, death, extrusion, neighbour exchange, and activity. Earlier studies on active systems have shown that activity has a non-trivial effect on this transition. For example, activity can introduce topological defects and oscillations, help in forming patterns, solidify or fluidize the tissue etc. Therefore, it is important to understand the role of activity in dense tissue. Theoretically speaking, any active system has two important factors: the magnitude of the active force and the persistent time of the force. The former determines the amount of the applied active force whereas the latter gives the time up to which the active force maintains a specific direction. However, due to experimental complexities, it is impossible to determine the origin of these parameters and control them precisely in actual cell monolayers.
Hence, in this work, we have introduced a synthetic active cellular model, composed of cells made of centimetre-sized bots within paper rings, where we can precisely control both of these active parameters. This is remarkable as this minimalistic model of synthetic cells would give deeper insights into the active cellular systems. We have observed a cellular shape-mediated transition when the persistence time of the active force was gradually increased; first, when the persistence time is small, the cell monolayer behaves like jammed glass, then at intermediate values of the persistence time, it goes into an unjammed liquid-like states, then again for large persistence time, it goes again into solid glass-like phase. In the jammed glassy states, the cells are caged by the other cells and in the unjammed fluid-like states they move rapidly.
Fluctuations are inherent in biological systems. However, in most of the experiments, these fluctuations are mostly regarded as biological noise until recently. In a seminal work, Atia et. al. [Nature Physics, 2018] have reported that the fluctuations in cell shape have a strong correlation with the mean cell shape across diverse classes of epithelial systems in a broad length scale, starting from Drosophila fruit fly embryonic cells to Human bronchial epithelial cells. This makes the correlation universal. However, what is the origin of this universality is unknown.
To answer this, recently [Sadhukhan and Nandi, eLife, 2022], we have developed the theory of cell shape, characterised by the aspect ratio (AR) of the cells. We found that the probability distribution function (PDF) of AR depends on a single parameter that governs both statics and dynamical properties of a cell monolayer, leading to a universal relationship between the fluctuations in cell shape and mean cell shape. Our predicted theoretical line explains previously reported experimental data on various cell types starting from cancerous cells to asthmatic and non-asthmatic bronchial cells, MDCK cells etc. This explains the origin of the universality in the cell shape fluctuations (measured by the standard deviation of AR, sd(AR)) and mean cell shapes (<AR>).
Close to a glassy regime, confluent cellular systems exhibit a phenomenon called Dynamical heterogeneity where some parts of the cells in the monolayer are moving faster than the other parts. Within our synthetic cellular model, we observed that although the fast cells have a large mean shape, implying they are elongated, they have less fluctuations compared to the universal relation. Thus, the points in the sd(AR) vs. <AR> deviate from the universal line. As fast cells are more dynamic than slow cells, one would expect large fluctuations in cell shapes, but the results seem to suggest the opposite. We answered this question numerically via simulations on a well-known model of confluent cell monolayer, the Cellular Potts model (CPM). We showed that the reduced cell shape fluctuations are a result of the confinement effect; in the glassy regime, fast cells are caged by slow-moving cells and these slow cells create an amorphous boundary for the fast cells, restricting their fluctuations in cell shape.
The deviation from this universal relation has several consequences regarding the statics and the dynamical properties of a confluent cell monolayer. For example, during cancer progression, some epithelial cells are more dynamic than others in the solid-like firmly connected cell monolayer. A local cell shape-based analysis will help in identifying these migrating cancerous cells within the cell monolayer.
Moreover, this synthetic model of confluent cell monolayer can be a useful tool in understanding biological processes such as cell sorting, and collective cell migration, purely from a geometrical/mechanical perspective. Within this model, we can control cell shape anisotropy, inter-cellular friction, motility, speed etc., which allows us to investigate the above-mentioned processes more microscopically in a detailed manner.
This work is published in Nature Communications and it is Featured as an Editor's Highlight in Applied Physics and Mathematics.
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