Mathematical and Computational Modeling of the Active Mechanics of Multicellular Systems: from Cell–Cell Adhesion to Tissue Reshaping

  • BAL, PRADEEP KUMAR (Polytechnic University of Catalonia (UPC Barc)
  • ARROYO, MARINO (Polytechnic University of Catalonia (UPC Barc)

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Cell–cell adhesion and tissue reshaping are fundamental active mechanical processes in multicellular systems. Although these processes originate at the subcellular level, they manifest at mesoscopic scales, posing significant challenges for theoretical and computational modeling. This talk explores several frameworks aimed at bridging this gap by capturing essential physical and biological mechanisms across scales, with a focus on (1) epithelial reshaping and (2) the guidance of cellular nematics elastomers to create shape-programmable living surfaces. To understand the emergent tissue mechanics arising from subcellular mechanisms, the talk first presents a fully nonlinear Cosserat continuum theory for epithelial shells that coarse-grains an underlying 3D vertex model whose cellular surfaces are modeled as active viscoelastic gels undergoing turnover. The framework incorporates junctional tilt, cortical viscoelasticity, and viscous interactions with the surrounding medium, and is implemented numerically using finite element methods. Applications include the study of morphogenesis driven by apico–basal tension asymmetries, as well as buckling and wrinkling in epithelial domes under rapid deflation. We show that epithelial buckling emerges from the interplay between active contractility, cortical viscoelasticity, viscous drag, and curvature anisotropy, leading to multiscale folding and wrinkling patterns. By introducing anisotropic curvature, we further demonstrate controlled symmetry breaking and predictable wrinkle organization. Finally, the talk discusses a strategy for engineering living tissues that autonomously morph into predefined 3D shapes by harnessing the nematic organization of cellular forces in fibroblast monolayers. Spatially patterned topological defects guide morphogenetic transformations through anisotropic in-plane contractile tensions, rather than through active flows or compressive buckling. Finite element simulations based on a contractile nematic thin-shell model accurately predict the experimentally observed deformations. This approach offers a robust and programmable framework for designing bioengineered tissues, synthetic morphogenesis, and soft robotic systems.