Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2015 | 3 | 1 |
Tytuł artykułu

Membrane-Channel Protein System Mesh Construction for Finite Element Simulations

Treść / Zawartość
Warianty tytułu
Języki publikacji
We present a method of constructing the volume meshes of the membrane-channel protein system for finite element simulation of ion channels. The membrane channel system consists of the solvent region and the membrane-protein region. Our method focuses on labeling the tetrahedra in the solvent and membrane-protein regions and collecting the interface triangles between different regions. It contains two stages. Firstly, a volume mesh conforming the surface of the channel protein is generated by the surface and volume mesh generation tools: TMSmesh and TetGen. Then a walk-and-detect algorithm is used to identify the pore region to embed the membrane correctly. This method is shown to be robust because of its independence of the pore structure of the ion channels. In addition, we can also get the information of whether the ion channel is open or closed by the walk-and-detect algorithm. An on-line meshing procedure will be available at our website
Opis fizyczny
  • State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science,
    National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing 100190, China
  • State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science,
    National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing 100190, China
  • National Center for NanoScience and Technology, Chinese Academy of Sciences, Beijing 100190, China
  • Center for System Biology, Department of Mathematics, Soochow University, Suzhou 215006, China
  • State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science,
    National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing 100190, China
  • [1] D. Marx and J. Hutter. Modern Methods and Algorithms of Quantum Chemistry. John von Neumann Institute for Computing,J¨ulich, 2000.
  • [2] J. Ostmeyer, S. Chakrapani, A. C. Pan, E. Perozo, and B. Roux. Recovery from slow inactivation in K+ channels is controlledby water molecules. Nature, 501(7465):121–124, 2013.[WoS]
  • [3] M. Jensen, V. Jogini, D. W. Borhani, A. E. Leffler, R. O. Dror, and D. E. Shaw. Mechanism of voltage gating in potassiumchannels. Science, 336(6078):229–233, 2012.
  • [4] S. Li, M. Hoyles, S. Kuyucak, and S. Chung. Brownian dynamics study of ion transport in the vestibule of membrane channels.Biophys. J., 74:37–47, 1998.[Crossref]
  • [5] B. Corry, S. Kuyucak, and S. H. Chung. Tests of continuum theories as models of ion channels. II. Poisson-Nernst-Plancktheory versus brownian dynamics. Biophys. J., 78:2364–2381, 2000.[Crossref]
  • [6] S. Kuyucak, O. S. Andersen, and S. H. Chung. Models of permeation in ion channels. Rep. Prog. Phys., 64:1427–1472, 2001.[Crossref]
  • [7] G. A. Huber and J. A. McCammon. Browndye: A software package for brownian dynamics. Comp. Phys. Comm., 181:1896–1905, 2010.[Crossref]
  • [8] B. Z. Lu and Y. C. Zhou. Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes II: Sizeeffects on ionic distributions and diffusion-reaction rates. Biophys. J., 100(10):2475 – 2485, 2011.[WoS][Crossref]
  • [9] B. Z. Lu. Poisson-Nernst-Planck equations. Encyclopedia of Applied and Computational Mathematics; Engquist, B., Ed.;Springer-Verlag: Berlin Heidelberg, 2013.
  • [10] B. Roux, T. Allen, S. Berneche, andW. Im. Theoretical and computational models of biological ionchannels. Q. Rev. Biophys.,7(1):1–103, 2004.
  • [11] R. S. Eisenberg. Ionic channels in biological membranes: natural nanotubes. Acc. Chem. Res., 31:117–123, 1998.[Crossref]
  • [12] D. Chen, J. Lear, and R. S. Eisenberg. Permeation through an open channel: Poisson-Nernst-Planck theory of a syntheticionic channel. Biophys. J., 72:97–116, 1997.[Crossref]
  • [13] M. G. Kurnikova, R. D. Coalson, P. Graf, and A. Nitzan. A lattice relaxation algorithm for three-dimensional Poisson-Nernst-Planck theory with application to ion transport through the gramicidin a channel. Biophys. J., 76:642–656, 1999.[Crossref]
  • [14] Q. Zheng, D. Chen, and G. W. Wei. Second-order Poisson-Nernst-Planck solver for ion transport. J. Comput. Phys.,230(13):5239–5262, 2011.[WoS][Crossref]
  • [15] B. Z. Lu, M. J. Holst, J. A. McCammon, and Y. C. Zhou. Poisson-Nernst-Planck equations for simulating biomolecular diffusionreactionprocesses I: Finite element solutions. J. Comput. Phys., 229(19):6979–6994, 2010.
  • [16] B. Z. Lu and J. A. McCammon. Molecular surface-free continuum model for electrodiffusion processes. Chem. Phys. Lett.,451(4-6):282–286, 2008.[WoS]
  • [17] B. Z. Lu, Y. C. Zhou, Gary A. Huber, S. D. Bond, Michael J. Holst, and J. A. McCammon. Electrodiffusion: A continuummodelingframework for biomolecular systems with realistic spatiotemporal resolution. J. Chem. Phys., 127(13):135102, 2007.[WoS]
  • [18] B. Tu, M. X. Chen, Y. Xie, L. B. Zhang, B. Eisenberg, and B.Z. Lu. A parallel finite element simulator for ion transport throughthree-dimensional ion channel systems. J. Comput. Chem., 34:2065–2078, 2013.[Crossref][WoS]
  • [19] B. Tu, S. Y. Bai, M. X. Chen, Y. Xie, L. B. Zhang, and B. Z. Lu. A software platform for continuum modeling of ion channelsbased on unstructured mesh. Computational Science & Discovery, 7:014002, 2014.
  • [20] U. Hollerbach, D. P. Chen, and R. S. Eisenberg. Two- and three-dimensional Poisson-Nernst-Planck simulations of currentflow through gramicidin a. J. Sci. Comput., 16(4):373–409, 2002.[Crossref]
  • [21] S. R. Mathur and J. Y. Murthy. A multigrid method for the Poisson-Nernst-Planck equations. SIAM J. Appl. Math., 52(17–18):4031–4039, 2009.
  • [22] M. X. Chen and B. Z. Lu. TMSmesh: A robust method for molecular surface mesh generation using a trace technique. J.Chem. Theory Comput., 7:203–212, 2011.[WoS][Crossref]
  • [23] M. X. Chen, B. Tu, and B. Z. Lu. Triangulated manifold meshing method preserving molecular surface topology. Journal ofMolecular Graphics and Modelling, 38:411–418, 2012.
  • [24] M. Sanner, A. Olson, and J. Spehner. Reduced surface: An eflcient way to compute molecular surface properties. Biopolymers,38:305–320, 1996.[Crossref]
  • [25] S. Decherchi and W. Rocchia. A general and robust ray casting based algorithm for triangulating surfaces at the nanoscale.PLoS One, 8(4):e59744, 2013.
  • [26] C. Bajaj, G. Xu, and Q. Zhang. Bio-molecule surfaces construction via a higher-order level-set method. Journal of ComputerScience and Technology, 23(6):1026–1036, 2008.[Crossref][WoS]
  • [27] W. Zhao, G. Xu, and C. Bajaj. An algebraic spline model of molecular surfaces for energetic computations. IEEE/ACM Transactionson Computational Biology and Bioinformatics, 8(6):1458–1467, 2011.[WoS][Crossref]
  • [28] Z.Y. Yu, M. J. Holst, and J. McCammon. High-fidelity geometric modeling for biomedical applications. Finite Elem. Anal. Des.,44(11):715–723, 2008.[WoS]
  • [29] D. Xu and Y. Zhang. Generating triangulated macromolecular surfaces by Euclidean Distance Transform. PLoS ONE,4(12):e8140, 2009.[WoS]
  • [30] B. Lee and F.M. Richards. The interpretation of protein structures: estimation of static accessibility. J.Mol. Biol., 55(3):379–400, 1971.[Crossref]
  • [31] F. M. Richards. Areas, volumes, packing and protein structure. Annual Review in Biophysics and Bioengineering, 6:151–176,1977.
  • [32] Y.J. Zhang, G.L. Xu, and C. Bajaj. Quality meshing of implicit solvation models of biomolecular structures. Comput. AidedGeom. Des, 23(6):510–530, 2006.
  • [33] H. Edelsbrunner. Deformable smooth surface design. Discrete and Computational Geometry, 21:87–115, 1999.[Crossref]
  • [34] A. Zaharescu, E. Boyer, and R. P. Horaud. Transformesh: a topology-adaptive mesh-based approach to surface evolution. InProceedings of the Eighth Asian Conference on Computer Vision, II:166–175, November 2007.
  • [35] H. Si. Tetgen, a Delaunay-based quality tetrahedral mesh generator. ACM Transactions on Mathematical Software, 41(2).[WoS]
  • [36] Oliver S. Smart, Joseph G. Neduvelil, Xiaonan Wang, B.A. Wallace, and Mark S.P. Sansom. Hole: A program for the analysisof the pore dimensions of ion channel structural models. Journal of Molecular Graphics, 14(6):354 – 360, 1996.[Crossref]
  • [37] S.Y. Bai and B.Z. Lu. VCMM: A visual tool for continuum molecular modeling. Journal of Molecular Graphics and Modelling,55:44–49, 2014.
  • [38] O. Devillers, S. Pion, and M. Teillaud. Walking in a triangulation. International Journal of Foundations of Computer Science,13(02):181–199, 2002.
  • [39] O. S. Andersen. Gramicidin channels. Annu. Rev. Physiol., 46:531–548, 1984.[Crossref]
  • [40] R. E. Koeppe and O. S. Andersen. Engineering the gramicidin channel. Annu. Rev. Biophys. Biomol. Struct., 25:231–258,1996.[Crossref]
  • [41] S. Maeda, S. Nakagawa, M. Suga, E. Yamashita, A. Oshima, Y. Fujiyoshi, and T. Tsukihara. Structure of the connexin 26 gapjunction channel at 3.5Å resolution. Nature, 458(7238):579–602, 2009.
  • [42] T. J. Dolinsky, J. E. Nielsen, J. A. McCammon, and N. A. Baker. PDB2PQR: an automated pipeline for the setup, execution,and analysis of poisson-boltzmann electrostatics calculations. Nucleic Acids Res., 32:W665–W667, 2004.
  • [43] A. Liu and B. Joe. Relationship between tetrahedron shape measures. BIT Numerical Mathematics, 34(2):268–287, 1994.[Crossref]
  • [44] Tiantian Liu, Minxin Chen, and Benzhuo Lu. Parameterization for molecular gaussian surface and a comparison study ofsurface mesh generation. Journal of Molecular Modeling, 21(5), 2015.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.