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Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions

100%
Liao T., Lee H.-C., Yang G., Zhang Y. J.
Molecular Based Mathematical Biology
|
2015
|
tom 3
|
nr 1
EN
The functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the order of modes. An initial correspondence is built based on the distribution of a shape diameter, which matches similar surface features in different shapes and guides the eigenfunction computation. A two-step scheme is developed to determine the final correspondence. The first step utilizes volumetric eigenfunctions to correct the assignment of boundary nodes that disobeys the main structures. The second step minimizes the distortion induced by deforming one shape to the other. As a result, a dense point correspondence is constructed between the two given shapes, based on which we approximate and predict the shape deformation, as well as quantitatively measure the detailed shape differences.
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Multi-core CPU or GPU-accelerated Multiscale Modeling for Biomolecular Complexes

64%
Liao T., Zhang Y., Kekenes-Huskey P. M., Cheng Y., Michailova A., McCulloch A. D., Holst M., McCammon J. A.
Molecular Based Mathematical Biology
|
2013
|
tom 1
164-179
EN
Multi-scale modeling plays an important role in understanding the structure and biological functionalities of large biomolecular complexes. In this paper, we present an efficient computational framework to construct multi-scale models from atomic resolution data in the Protein Data Bank (PDB), which is accelerated by multi-core CPU and programmable Graphics Processing Units (GPU). A multi-level summation of Gaussian kernel functions is employed to generate implicit models for biomolecules. The coefficients in the summation are designed as functions of the structure indices, which specify the structures at a certain level and enable a local resolution control on the biomolecular surface. A method called neighboring search is adopted to locate the grid points close to the expected biomolecular surface, and reduce the number of grids to be analyzed. For a specific grid point, a KD-tree or bounding volume hierarchy is applied to search for the atoms contributing to its density computation, and faraway atoms are ignored due to the decay of Gaussian kernel functions. In addition to density map construction, three modes are also employed and compared during mesh generation and quality improvement to generate high quality tetrahedral meshes: CPU sequential, multi-core CPU parallel and GPU parallel. We have applied our algorithm to several large proteins and obtained good results.
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