Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff–Love kinematicsand revealed by a three-dimensional computational framework
| Autor: | Krishna Garikipati, Rahul Gulati, Debabrata Auddya, Xiaoxuan Zhang, Shiva Rudraraju, Padmini Rangamani, Ritvik Vasan |
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| Rok vydání: | 2021 |
| Předmět: |
1.1 Normal biological development and functioning
General Mathematics Rotational symmetry FOS: Physical sciences Boundary (topology) General Physics and Astronomy Kinematics Isogeometric analysis Condensed Matter - Soft Condensed Matter Deformation (meteorology) Quantitative Biology - Quantitative Methods 01 natural sciences Mathematical Sciences Quantitative Biology::Cell Behavior 010305 fluids & plasmas Quantitative Biology::Subcellular Processes 03 medical and health sciences Engineering 0103 physical sciences Computational mechanics endocytosis Symmetry breaking Boundary value problem 0101 mathematics Quantitative Methods (q-bio.QM) 030304 developmental biology Physics FEM Physics::Biological Physics 0303 health sciences General Engineering biomembranes Mechanics Nerve Impulses Kirchhoff-Love Finite element method 010101 applied mathematics isogeometric analysis Endocytic vesicle Classical mechanics Transmission (telecommunications) FOS: Biological sciences Physical Sciences Soft Condensed Matter (cond-mat.soft) non-axisymmetric |
| Zdroj: | Proceedings. Mathematical, physical, and engineering sciences, vol 477, iss 2255 |
| ISSN: | 1471-2946 1364-5021 |
| DOI: | 10.1098/rspa.2021.0246 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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