Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry
Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared with approximation-based methods (e.g., finite element method [FEM]), the cla...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-09-01
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| Series: | Biophysical Reports |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2667074722000192 |
| _version_ | 1828299631993290752 |
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| author | Cuncheng Zhu Christopher T. Lee Padmini Rangamani |
| author_facet | Cuncheng Zhu Christopher T. Lee Padmini Rangamani |
| author_sort | Cuncheng Zhu |
| collection | DOAJ |
| description | Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared with approximation-based methods (e.g., finite element method [FEM]), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on discrete differential geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid; and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions. |
| first_indexed | 2024-04-13T12:57:33Z |
| format | Article |
| id | doaj.art-3fc4a7a922e749f6afe5f31d05c256aa |
| institution | Directory Open Access Journal |
| issn | 2667-0747 |
| language | English |
| last_indexed | 2024-04-13T12:57:33Z |
| publishDate | 2022-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Biophysical Reports |
| spelling | doaj.art-3fc4a7a922e749f6afe5f31d05c256aa2022-12-22T02:46:01ZengElsevierBiophysical Reports2667-07472022-09-0123100062Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometryCuncheng Zhu0Christopher T. Lee1Padmini Rangamani2Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla CA 92093Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla CA 92093; Corresponding authorDepartment of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla CA 92093; Corresponding authorBiomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared with approximation-based methods (e.g., finite element method [FEM]), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on discrete differential geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid; and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions.http://www.sciencedirect.com/science/article/pii/S2667074722000192 |
| spellingShingle | Cuncheng Zhu Christopher T. Lee Padmini Rangamani Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry Biophysical Reports |
| title | Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry |
| title_full | Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry |
| title_fullStr | Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry |
| title_full_unstemmed | Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry |
| title_short | Mem3DG: Modeling membrane mechanochemical dynamics in 3D using discrete differential geometry |
| title_sort | mem3dg modeling membrane mechanochemical dynamics in 3d using discrete differential geometry |
| url | http://www.sciencedirect.com/science/article/pii/S2667074722000192 |
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