Constructing Triangular Meshes of Minimal Area

Chen, Wenyu; Cai, Yiyu; Zheng, Jianmin

doi:10.3722/cadaps.2008.508-518

Cited by 17 publications

(6 citation statements)

References 22 publications

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“…In our work we implemented an algorithm discussed in ref. 47. The initial data in this algorithm consists of coordinates of amino acids in the covalent loop.…”

Section: Methodsmentioning

confidence: 99%

Complex lasso: new entangled motifs in proteins

Niemyska

Dąbrowski-Tumański

Kadlof

et al. 2016

Sci Rep

108

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We identify new entangled motifs in proteins that we call complex lassos. Lassos arise in proteins with disulfide bridges (or in proteins with amide linkages), when termini of a protein backbone pierce through an auxiliary surface of minimal area, spanned on a covalent loop. We find that as much as 18% of all proteins with disulfide bridges in a non-redundant subset of PDB form complex lassos, and classify them into six distinct geometric classes, one of which resembles supercoiling known from DNA. Based on biological classification of proteins we find that lassos are much more common in viruses, plants and fungi than in other kingdoms of life. We also discuss how changes in the oxidation/reduction potential may affect the function of proteins with lassos. Lassos and associated surfaces of minimal area provide new, interesting and possessing many potential applications geometric characteristics not only of proteins, but also of other biomolecules.

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“…In our work we implemented an algorithm discussed in ref. 47. The initial data in this algorithm consists of coordinates of amino acids in the covalent loop.…”

Section: Methodsmentioning

confidence: 99%

Complex lasso: new entangled motifs in proteins

Niemyska

Dąbrowski-Tumański

Kadlof

et al. 2016

Sci Rep

108

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“…The algorithm relies on coordinates of Cα atoms (from the PDB file) or any atoms/monomers (in XYZ file). The triangulated surface of minimal area (called a minimal surface) is spanned on the closed loop following techniques in computer graphics ( 13 ); our algorithm, optimized for proteins and taking into account surface orientation (to detect supercoiling), gives the same results as established software (e.g. Surface Evolver ( 14 )).…”

Section: Methodsmentioning

confidence: 99%

LassoProt: server to analyze biopolymers with lassos

Dąbrowski-Tumański¹,

Niemyska

Pasznik³

et al. 2016

Nucleic Acids Res

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The LassoProt server, http://lassoprot.cent.uw.edu.pl/, enables analysis of biopolymers with entangled configurations called lassos. The server offers various ways of visualizing lasso configurations, as well as their time trajectories, with all the results and plots downloadable. Broad spectrum of applications makes LassoProt a useful tool for biologists, biophysicists, chemists, polymer physicists and mathematicians. The server and our methods have been validated on the whole PDB, and the results constitute the database of proteins with complex lassos, supported with basic biological data. This database can serve as a source of information about protein geometry and entanglement-function correlations, as a reference set in protein modeling, and for many other purposes.

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“…A minimal area mesh can be constructed using the vertexbased algorithm, which minimizes the total area of the surface by minimizing the area around each vertex [10]. However, with such an algorithm, the triangles comprising the resection surface cannot guarantee the safety margin.…”

Section: E Resection Construction and Optimizationmentioning

confidence: 99%

Planning of hepatectomy for tumor resection: Resection surface construction and optimization

Chen

Zhou

Xiong

et al. 2013

2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

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An interactive liver surgery planning system has been developed to construct and optimize the resection plan. With this system, the segmentation results of the liver and its components (such as tumors and vessels) are comprehensively visualized for surgeons to have an intuitive understanding of the internal anatomical structure of the liver. This system will also allow surgeons to interactively create and modify a resection plan on the virtual liver model. The resection surface, whose boundary is a closed curve, will be automatically constructed with the safe resection margins of tumors. Different from other systems, our developed system is able to generate the safety margins to all tumors. During surgery, a larger resection surface may cause potentially more bleeding and other complications. Therefore, area minimization is applied during the resection surface construction by adopting the minimal area mesh, which is a smooth surface with minimal area. After these virtual modifications, the resultant resection surface indicates the route to cut the liver for tumor removal. The volumes for both resected liver and residual liver are calculated for clinical decision making.

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Constructing Triangular Meshes of Minimal Area

Cited by 17 publications

References 22 publications

Complex lasso: new entangled motifs in proteins

Complex lasso: new entangled motifs in proteins

LassoProt: server to analyze biopolymers with lassos

Planning of hepatectomy for tumor resection: Resection surface construction and optimization

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