1
|
Liu Z, Gui S, Lu B, Zhang L. An Unfitted Finite Element Poisson-Boltzmann Solver with Automatic Resolving of Curved Molecular Surface. J Phys Chem B 2024; 128:6463-6475. [PMID: 38949996 DOI: 10.1021/acs.jpcb.4c01894] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/03/2024]
Abstract
So far, the existing Poisson-Boltzmann (PB) solvers that accurately take into account the interface jump conditions need a pregenerated body-fitted mesh (molecular surface mesh). However, qualified biomolecular surface meshing and its implementation into numerical methods remains a challenging and laborious issue, which practically hinders the progress of further developments and applications of a bunch of numerical methods in this field. In addition, even with a molecular surface mesh, it is only a low-order approximation of the original curved surface. In this article, an interface-penalty finite element method (IPFEM), which is a typical unfitted finite element method, is proposed to solve the Poisson-Boltzmann equation (PBE) without requiring the user to generate a molecular surface mesh. The Gaussian molecular surface is used to represent the molecular surface and can be automatically resolved with a high-order approximation within our method. Theoretical convergence rates of the IPFEM for the linear PB equation have been provided and are well validated on a benchmark problem with an analytical solution (we also noticed from numerical examples that the IPFEM has similar convergence rates for the nonlinear PBE). Numerical results on a set of different-sized biomolecules demonstrate that the IPFEM is numerically stable and accurate in the calculation of biomolecular electrostatic solvation energy.
Collapse
Affiliation(s)
- Ziyang Liu
- ICMSEC, LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Sheng Gui
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
| | - Benzhuo Lu
- ICMSEC, LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Linbo Zhang
- ICMSEC, LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| |
Collapse
|
2
|
Abdellah M, Cantero JJG, Guerrero NR, Foni A, Coggan JS, Calì C, Agus M, Zisis E, Keller D, Hadwiger M, Magistretti PJ, Markram H, Schürmann F. Ultraliser: a framework for creating multiscale, high-fidelity and geometrically realistic 3D models for in silico neuroscience. Brief Bioinform 2022; 24:6847753. [PMID: 36434788 PMCID: PMC9851302 DOI: 10.1093/bib/bbac491] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2022] [Revised: 09/27/2022] [Accepted: 10/14/2022] [Indexed: 11/27/2022] Open
Abstract
Ultraliser is a neuroscience-specific software framework capable of creating accurate and biologically realistic 3D models of complex neuroscientific structures at intracellular (e.g. mitochondria and endoplasmic reticula), cellular (e.g. neurons and glia) and even multicellular scales of resolution (e.g. cerebral vasculature and minicolumns). Resulting models are exported as triangulated surface meshes and annotated volumes for multiple applications in in silico neuroscience, allowing scalable supercomputer simulations that can unravel intricate cellular structure-function relationships. Ultraliser implements a high-performance and unconditionally robust voxelization engine adapted to create optimized watertight surface meshes and annotated voxel grids from arbitrary non-watertight triangular soups, digitized morphological skeletons or binary volumetric masks. The framework represents a major leap forward in simulation-based neuroscience, making it possible to employ high-resolution 3D structural models for quantification of surface areas and volumes, which are of the utmost importance for cellular and system simulations. The power of Ultraliser is demonstrated with several use cases in which hundreds of models are created for potential application in diverse types of simulations. Ultraliser is publicly released under the GNU GPL3 license on GitHub (BlueBrain/Ultraliser). SIGNIFICANCE There is crystal clear evidence on the impact of cell shape on its signaling mechanisms. Structural models can therefore be insightful to realize the function; the more realistic the structure can be, the further we get insights into the function. Creating realistic structural models from existing ones is challenging, particularly when needed for detailed subcellular simulations. We present Ultraliser, a neuroscience-dedicated framework capable of building these structural models with realistic and detailed cellular geometries that can be used for simulations.
Collapse
Affiliation(s)
- Marwan Abdellah
- Corresponding authors. Marwan Abdellah, Blue Brain Project (BBP), École Polytechnique Fédérale de Lausanne (EPFL), Geneva, Switzerland. E-mail: ; Felix Schürmann, Blue Brain Project (BBP), École Polytechnique Fédérale de Lausanne (EPFL), Geneva, Switzerland. E-mail:
| | | | - Nadir Román Guerrero
- Blue Brain Project (BBP) École Polytecnique Fédérale de Lausanne (EPFL) Geneva, Switzerland
| | - Alessandro Foni
- Blue Brain Project (BBP) École Polytecnique Fédérale de Lausanne (EPFL) Geneva, Switzerland
| | - Jay S Coggan
- Blue Brain Project (BBP) École Polytecnique Fédérale de Lausanne (EPFL) Geneva, Switzerland
| | - Corrado Calì
- Biological and Environmental Sciences and Engineering Division King Abdullah University of Science and Technology (KAUST) Thuwal, Saudi Arabia,Neuroscience Institute Cavalieri Ottolenghi (NICO) Orbassano, Italy,Department of Neuroscience, University of Torino Torino, Italy
| | - Marco Agus
- Visual Computing Center King Abdullah University of Science and Technology (KAUST) Thuwal, Saudi Arabia,College of Science and Engineering Hamad Bin Khalifa University Doha, Qatar
| | - Eleftherios Zisis
- Blue Brain Project (BBP) École Polytecnique Fédérale de Lausanne (EPFL) Geneva, Switzerland
| | - Daniel Keller
- Blue Brain Project (BBP) École Polytecnique Fédérale de Lausanne (EPFL) Geneva, Switzerland
| | - Markus Hadwiger
- Visual Computing Center King Abdullah University of Science and Technology (KAUST) Thuwal, Saudi Arabia
| | - Pierre J Magistretti
- Biological and Environmental Sciences and Engineering Division King Abdullah University of Science and Technology (KAUST) Thuwal, Saudi Arabia
| | - Henry Markram
- Blue Brain Project (BBP) École Polytecnique Fédérale de Lausanne (EPFL) Geneva, Switzerland
| | - Felix Schürmann
- Corresponding authors. Marwan Abdellah, Blue Brain Project (BBP), École Polytechnique Fédérale de Lausanne (EPFL), Geneva, Switzerland. E-mail: ; Felix Schürmann, Blue Brain Project (BBP), École Polytechnique Fédérale de Lausanne (EPFL), Geneva, Switzerland. E-mail:
| |
Collapse
|
3
|
Khan D, Plopski A, Fujimoto Y, Kanbara M, Jabeen G, Zhang YJ, Zhang X, Kato H. Surface Remeshing: A Systematic Literature Review of Methods and Research Directions. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2022; 28:1680-1713. [PMID: 32795969 DOI: 10.1109/tvcg.2020.3016645] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Triangle meshes are used in many important shape-related applications including geometric modeling, animation production, system simulation, and visualization. However, these meshes are typically generated in raw form with several defects and poor-quality elements, obstructing them from practical application. Over the past decades, different surface remeshing techniques have been presented to improve these poor-quality meshes prior to the downstream utilization. A typical surface remeshing algorithm converts an input mesh into a higher quality mesh with consideration of given quality requirements as well as an acceptable approximation to the input mesh. In recent years, surface remeshing has gained significant attention from researchers and engineers, and several remeshing algorithms have been proposed. However, there has been no survey article on remeshing methods in general with a defined search strategy and article selection mechanism covering the recent approaches in surface remeshing domain with a good connection to classical approaches. In this article, we present a survey on surface remeshing techniques, classifying all collected articles in different categories and analyzing specific methods with their advantages, disadvantages, and possible future improvements. Following the systematic literature review methodology, we define step-by-step guidelines throughout the review process, including search strategy, literature inclusion/exclusion criteria, article quality assessment, and data extraction. With the aim of literature collection and classification based on data extraction, we summarized collected articles, considering the key remeshing objectives, the way the mesh quality is defined and improved, and the way their techniques are compared with other previous methods. Remeshing objectives are described by angle range control, feature preservation, error control, valence optimization, and remeshing compatibility. The metrics used in the literature for the evaluation of surface remeshing algorithms are discussed. Meshing techniques are compared with other related methods via a comprehensive table with indices of the method name, the remeshing challenge met and solved, the category the method belongs to, and the year of publication. We expect this survey to be a practical reference for surface remeshing in terms of literature classification, method analysis, and future prospects.
Collapse
|
4
|
Gui S, Khan D, Wang Q, Yan DM, Lu BZ. Frontiers in biomolecular mesh generation and molecular visualization systems. Vis Comput Ind Biomed Art 2018; 1:7. [PMID: 32240387 PMCID: PMC7099538 DOI: 10.1186/s42492-018-0007-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2018] [Accepted: 07/01/2018] [Indexed: 11/25/2022] Open
Abstract
With the development of biomolecular modeling and simulation, especially implicit solvent modeling, higher requirements are set for the stability, efficiency and mesh quality of molecular mesh generation software. In this review, we summarize the recent works in biomolecular mesh generation and molecular visualization. First, we introduce various definitions of molecular surface and corresponding meshing software. Second, as the mesh quality significantly influences biomolecular simulation, we investigate some remeshing methods in the fields of computer graphics and molecular modeling. Then, we show the application of biomolecular mesh in the boundary element method (BEM) and the finite element method (FEM). Finally, to conveniently visualize the numerical results based on the mesh, we present two types of molecular visualization systems.
Collapse
Affiliation(s)
- Sheng Gui
- LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China.
- University of Chinese Academy of Sciences, Beijing, 100049, China.
| | - Dawar Khan
- National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Qin Wang
- LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Dong-Ming Yan
- National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Ben-Zhuo Lu
- LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| |
Collapse
|