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Alpha shape and Delaunay triangulation in studies of protein-related interactions
2012
Briefings in Bioinformatics
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This review presents state-of-the-art applications of alpha shape and Delaunay triangulation in the studies on protein^DNA, protein^protein, protein^ligand interactions and protein structure analysis. ...
In recent years, more 3D protein structures have become available, which has made the analysis of large molecular structures much easier. ...
[61, 62] develop CAVER and MOLE, which use convex hull and Voronoi diagram to represent the protein structure, respectively. ...
doi:10.1093/bib/bbs077
pmid:23193202
fatcat:fp3mdawlsra7bc7je5t4bgyhji
Revisiting the Voronoi description of protein-protein interfaces
2006
Protein Science
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We developed a model of macromolecular interfaces based on the Voronoi diagram and the related alpha-complex, and we tested its properties on a set of 96 protein-protein complexes taken from the Protein ...
The Voronoi model provides robust definitions of the curvature and of the connectivity of the interfaces, and leads to estimates of these features that generally agree with other approaches. ...
predict complexes when little or no structural information on the partners is known. ...
doi:10.1110/ps.062245906
pmid:16943442
pmcid:PMC2242599
fatcat:dsadnchnrrf7dn3la6s7fo3pnm
Shelling the Voronoi interface of protein-protein complexes predicts residue activity and conservation
2008
Nature Precedings
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We show that patterns of 'dry' residues can, to a large extent, be predicted by a fast, parameter-free and purely geometric analysis of protein interfaces. ...
We analyze the correlation between Voronoi shelling order, dryness, and conservation on a set of 54 protein-protein complexes. ...
We would like to express our gratitude to Olivier Lichtarge ...
doi:10.1038/npre.2008.1522.2
fatcat:oeolsiosfzdx3ikan4e73n2tee
Molecular Cavity Topological Representation for Pattern Analysis: A NLP Analogy-Based Word2Vec Method
2019
International Journal of Molecular Sciences
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On a real data set, we demonstrate that our approach is applicable to maintain the topological characteristics of the cavity and can find the change patterns from a large number of cavities. ...
Then, we use some techniques such as dimension reduction and clustering to conduct an exploratory analysis of the vectorized molecular cavity. ...
The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. ...
doi:10.3390/ijms20236019
pmid:31795343
pmcid:PMC6928730
fatcat:vxme5vblcrbm7g5en3dh25t7ly
Conformational Flexibility of Pyruvate Dehydrogenase Complexes: A Computational Analysis by Quantized Elastic Deformational Model
2003
Journal of Molecular Biology
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Structural details of the motions of the trimeric building blocks, which are critical to facilitating the global expansion and contraction of the complex, were revealed. ...
Moreover, the current results support an earlier suggestion that, at low resolution and without the use of amino acid sequence and atomic coordinates, it is possible for computer simulations to provide ...
Acknowledgements This research was supported, in part, by grants from the American Heart Association (AHA- ...
doi:10.1016/s0022-2836(03)00555-2
pmid:12818207
fatcat:cnzqcarptvcgrbjo77gyra44ke
A boundary-partition-based Voronoi diagram of d-dimensional balls: definition, properties, and applications
2020
Advances in Computational Mathematics
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In computational geometry, different ways of space partitioning have been developed, including the Voronoi diagram of points and the power diagram of balls. ...
The definition, properties, and applications of this diagram are presented. ...
We have studied the properties of this diagram and presented its applications. ...
doi:10.1007/s10444-020-09765-3
fatcat:ta4dt2cehzdrxotdjviiuwbycq
Geometric filtering of pairwise atomic interactions applied to the design of efficient statistical potentials
2006
Computer Aided Geometric Design
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We show that we can filter the list of all interactions in a protein to generate a much smaller subset of pairs that retains most of the structural information contained in proteins. ...
Distance-dependent, pairwise, statistical potentials are based on the concept that the packing observed in known protein structures can be used as a reference for comparing different 3D models for a protein ...
Acknowledgments Research of all authors is partially supported by NSF under grant CCR-00-86013. ...
doi:10.1016/j.cagd.2006.03.002
fatcat:ecz55bxysfb4baclknmcxelgsu
Geometric measures of large biomolecules: Surface, volume, and pockets
2011
Journal of Computational Chemistry
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As an example, it takes 136 seconds with UnionBall to compute the contribution of each atom to the surface area and volume of a viral capsid with more than five million atoms on a commodity PC. ...
In addition, the detection of pockets serves as a starting point for predictive studies of biomolecule-ligand interactions. ...
P.K. acknowledges current support from the NIH under contract GM080399. ...
doi:10.1002/jcc.21884
pmid:21823134
pmcid:PMC3188685
fatcat:onuc4dfosfdnrhooaxbwaieqxu
Three-dimensional alpha shapes
[article]
1994
arXiv
pre-print
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Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the "shape" of the set. ...
A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned. ...
We are also indebted to Marc Dyksterhouse, Eric Jakobson, Patrick Moran, Michael Norman, and Shankar Subramanian from NCSA for their valuable comments and interest in our work, and the sta at the NCSA ...
arXiv:math/9410208v1
fatcat:eg6tjldi3nhs5hpofjbimbiy2e
The Role of the Antigen GAD 65 in Diabetes Mellitus Type 1: A Molecular Analysis
[chapter]
2012
Autoimmune Diseases - Contributing Factors, Specific Cases of Autoimmune Diseases, and Stem Cell and Other Therapies
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as to any other ball: 3 : ( ) ( ) i j i j V x π x π x (38) Each Voronoi cell is an intersection of closed half-spaces and therefore a convex polyhedron. ...
Molecular analysis and visualization Functional specificity and biological function of a protein are linked to its structure. ...
The coefficients nμ c define the contribution of the atomic orbital's to the molecular orbitals and are the weight of the μ -the atomic orbital in the n-te molecular orbital ( Figure 23D ). ...
doi:10.5772/48329
fatcat:xmbw67cymzbsdkyyzwt2u3maze
Characterizing the morphology of protein binding patches
2012
Proteins: Structure, Function, and Bioinformatics
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Finally, we exhibit a descriptor outperforming its contenders to predict the binding anities of the anity benchmark. ...
To improve our understanding of the structure-function relationship, we present a patch model decoupling the topological and geometric properties. ...
Let the restriction of a ball B i be the 3D region dened by the intersection between B i and its Voronoi region. ...
doi:10.1002/prot.24144
pmid:22806945
fatcat:tkfvofwweff5dmhpxrg2guzlyu
Indexing 3D Scenes Using the Interaction Bisector Surface
2014
ACM Transactions on Graphics
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In this paper we propose a new method for the classification and retrieval of 3D objects based on the Interaction Bisector Surface (IBS), a subset of the Voronoi diagram defined between objects. ...
We propose a hierarchical framework to index scenes by examining both the topological structure and the geometric attributes of the IBS. ...
We also thank Rami Ali Al-ashqar for his help in preparing 3d models used in Figure 1 and Figure 5 , Shin Yoshizawa for the discussions and the test-users for their help in evaluation of our system. ...
doi:10.1145/2574860
fatcat:srxkakwhrffj7inaoh2bnwze4u
Global and local Voronoi analysis of solvation shells of proteins
2010
Journal of Chemical Physics
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This paper presents the structure and dynamics of hydration shells for the three proteins: ubiquitin, calbindin, and phospholipase. ...
In order to cope with the high numerical effort for the computation of these Voronoi shells, we have implemented and optimized an intrinsically periodic algorithm. ...
ACKNOWLEDGMENTS This work was supported by the FWF Austrian Science Fund under Project No. P19807. ...
doi:10.1063/1.3471383
pmid:20815561
fatcat:yvqjwxiakvcothvskc575ypyt4
ProteinVolume: calculating molecular van der Waals and void volumes in proteins
2015
BMC Bioinformatics
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Voids and cavities in the native protein structure determine the pressure unfolding of proteins. ...
In addition, the volume changes due to the interaction of newly exposed atoms with solvent upon protein unfolding also contribute to the pressure unfolding of proteins. ...
Acknowledgements This work was supported by the US National Science Foundation grant CHE-1145407 (Chemistry of Life Processes). ...
doi:10.1186/s12859-015-0531-2
pmid:25885484
pmcid:PMC4379742
fatcat:oh2yc5l2e5bcnbv7gs7ww3uxuu
Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges
2018
Journal of Computer-Aided Molecular Design
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Our predictions were ranked 1st in 10 out of 26 official competitive tasks. * Corresponding to Guo-Wei Wei. ...
It has 5 subchallenges involving Cathepsin S and five other kinase targets, namely VEGFR2, JAK2, p38-α, TIE2, and ABL1. There is a total of 26 official competitive tasks for GC3. ...
We utilized the homology modeling task in Maestro of Schrödinger software 44 to obtain 3D structure predictions. ...
doi:10.1007/s10822-018-0146-6
pmid:30116918
fatcat:xvxlbafp4jhbxhhjmib44mdufm
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