2 research outputs found
Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematics and revealed by a three dimensional computational framework
Biomembranes play a central role in various phenomena like locomotion of
cells, cell-cell interactions, packaging of nutrients, and in maintaining
organelle morphology and functionality. During these processes, the membranes
undergo significant morphological changes through deformation, scission, and
fusion. Modeling the underlying mechanics of such morphological changes has
traditionally relied on reduced order axisymmetric representations of membrane
geometry and deformation. Axisymmetric representations, while robust and
extensively deployed, suffer from their inability to model symmetry breaking
deformations and structural bifurcations. To address this limitation, a 3D
computational mechanics framework for high fidelity modeling of biomembrane
deformation is presented. The proposed framework brings together Kirchhoff-Love
thin-shell kinematics, Helfrich-energy based mechanics, and state-of-the-art
numerical techniques for modeling deformation of surface geometries. Lipid
bilayers are represented as spline-based surfaces immersed in a 3D space; this
enables modeling of a wide spectrum of membrane geometries, boundary
conditions, and deformations that are physically admissible in a 3D space. The
mathematical basis of the framework and its numerical machinery are presented,
and their utility is demonstrated by modeling 3 classical, yet non-trivial,
membrane problems: formation of tubular shapes and their lateral constriction,
Piezo1-induced membrane footprint generation and gating response, and the
budding of membranes by protein coats during endocytosis. For each problem, the
full 3D membrane deformation is captured, potential symmetry-breaking
deformation paths identified, and various case studies of boundary and load
conditions are presented. Using the endocytic vesicle budding as a case study,
we also present a "phase diagram" for its symmetric and broken-symmetry states
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Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematicsand revealed by a three-dimensional computational framework.
Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model-symmetry breaking deformations and structural bifurcations. To address this limitation, a three-dimensional computational mechanics framework for high fidelity modelling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff-Love thin-shell kinematics, Helfrich-energy-based mechanics, and state-of-the-art numerical techniques for modelling deformation of surface geometries. Lipid bilayers are represented as spline-based surface discretizations immersed in a three-dimensional space; this enables modelling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a three-dimensional space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modelling three classical, yet non-trivial, membrane deformation problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full three-dimensional membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a 'phase diagram' for its symmetric and broken-symmetry states