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

Abstract

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. 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 three-dimensional 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 surface discretizations immersed in a three-dimensional 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 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.

Formation of protein-mediated bilayer tubes is governed by a snapthrough transition

“…Simulations using general coordinates reveal that the early modes of deformation are axisymmetric (65). However, relaxation of the assumption of axisymmetry in tubulation would be necessary to investigate how forces and proteins may interact (65)(66)(67). In summary, we expect that the findings from our work will motivate the development of these future efforts and gain a deeper understanding of how membrane tubes form under different biophysical conditions.…”

“…We also anticipate that the interactions between protein-mediated tubulation and force-mediated tubulation would be necessary to capture cellular processes where both membrane-bound proteins and actin-mediated forces are involved (54). Finally, relaxation of the assumption of axisymmetry in tubulation could be necesary to investigate how forces and proteins may interact (55)(56)(57). In summary, we expect that the findings from our work will motivate the development of these future efforts and gain a deeper understanding of how membrane tubes form.…”