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Mr. Pradeep Kumar Bal is a PhD student at LaCàN’s Cell and Tissue Mechanobiology and Computational Biomechanics research line, under the supervision of Prof. Marino Arroyo. He is also a researcher at CIMNE’s Computational Mechanics in Medical Engineering and Living Matter research cluster.
This thesis develops theoretical and computational frameworks to model two fundamental mechanical functions of multicellular tissues: cell-cell adhesion and epithelial reshaping. These processes are controlled by sub-cellular dynamics, yet they manifest at mesoscopic scales, posing a challenge for existing models. The work is structured in two parts, each addressing a different aspect of tissue mechanics while sharing a common approach based on irreversible thermodynamics and active gel theory.
In Part I, the focus is on modeling the dynamic formation and organization of cell-cell adhesions, particularly between pairs of cells. A mesoscale theoretical model is developed that couples the mechanics of the cellular surface, chemical kinetics of adhesion molecules, their lateral diffusion on the membrane, and feedback with the actomyosin cortex. The framework relies on Onsager’s variational formalism to ensure thermodynamic consistency and is implemented computationally in both axisymmetric and 3D finite element formulations. Simulations reveal how mechano-chemical couplings (including the reduction of cortical contractility within adhesions, force-induced bond activation, and immobilization of activated bonds) drive the self-organization of mature adhesion patches. This work not only reproduces experimental observations of adhesion behavior but also sets the stage for future modeling of adhesion turnover, decohesion dynamics, and asymmetrical cell contacts.
Part II focuses on epithelial reshaping, a key driver of morphogenesis. We propose a continuum shell theory for epithelial monolayers derived from sub-cellular descriptions of the actin cortex as an active gel. Two formulations are introduced: a Kirchhoff shell theory with perpendicular lateral junctions, and a more general Cosserat theory that allows for junctional tilt. These models are implemented numerically using finite element methods and validated against 3D vertex simulations. Applications include the study of apico-basal asymmetries, buckling, and wrinkling in epithelial tissues, particularly under rapid deflation as in recent experimental setups. The continuum model demonstrates how cortical viscoelasticity, viscous drag by the surrounding medium, and curvature anisotropy determine the morphology and patterning of wrinkles in epithelial shells. Future directions include accounting for evolving junctional networks and for biochemical signaling.
Together, these contributions offer a mesoscale framework to bridge sub-cellular dynamics with tissue-scale mechanical behavior, providing mechanistic insight into processes central to tissue development, integrity, and morphogenesis.
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