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Biomembranes play a central role in various phenomena like locomotion ofcells, cell-cell interactions, packaging of nutrients, and in maintainingorganelle morphology and functionality. During these processes, the membranesundergo significant morphological changes through deformation, scission, andfusion. Modeling the underlying mechanics of such morphological changes hastraditionally relied on reduced order axisymmetric representations of membranegeometry and deformation. Axisymmetric representations, while robust andextensively deployed, suffer from their inability to model symmetry breakingdeformations and structural bifurcations. To address this limitation, a 3Dcomputational mechanics framework for high fidelity modeling of biomembranedeformation is presented. The proposed framework brings together Kirchhoff-Lovethin-shell kinematics, Helfrich-energy based mechanics, and state-of-the-artnumerical techniques for modeling deformation of surface geometries. Lipidbilayers are represented as spline-based surfaces immersed in a 3D space; thisenables modeling of a wide spectrum of membrane geometries, boundaryconditions, and deformations that are physically admissible in a 3D space. Themathematical 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 thebudding of membranes by protein coats during endocytosis. For each problem, thefull 3D membrane deformation is captured, potential symmetry-breakingdeformation paths identified, and various case studies of boundary and loadconditions are presented. Using the endocytic vesicle budding as a case study,we also present a "phase diagram" for its symmetric and broken-symmetry states.

proceedings - royal society. mathematical, physical and engineering sciences

Biomembranes undergo complex, non-axisymmetric deformations governed by  Kirchhoff-Love kinematics and revealed by a three dimensional computational  framework