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RISS 인기검색어
- 검색키워드
- 저자 : Coutsias, Evangelos A. (검색결과 5 건)
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Using quaternions to calculate RMSD
Coutsias, Evangelos A.,Seok, Chaok,Dill, Ken A. John Wiley Sons, Inc. 2004 Journal of computational chemistry Vol.25 No.15
<P>A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the root-mean-square deviation (RMSD). We present a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. We prove that the quaternion method is equivalent to the well-known formula due to Kabsch. We analyze the various cases that may arise, and give a complete enumeration of the special cases in terms of the arrangement of the eigenvalues of a traceless, 4 × 4 symmetric matrix. A key result here is an expression for the gradient of the RMSD as a function of model parameters. This can be useful, for example, in finding the minimum energy path of a reaction using the elastic band methods or in optimizing model parameters to best fit a target structure. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1849–1857, 2004</P> <B>Graphic Abstract</B> <img src='wiley_img/01928651-2004-25-15-JCC20110-gra001.gif' alt='wiley_img/01928651-2004-25-15-JCC20110-gra001'>
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Efficiency of Rotational Operators for Geometric Manipulation of Chain Molecules
Seok, Chaok,Coutsias, Evangelos A. Korean Chemical Society 2007 Bulletin of the Korean Chemical Society Vol.28 No.10
Geometric manipulation of molecules is an essential elementary component in computational modeling programs for molecular structure, stability, dynamics, and design. The computational complexity of transformation of internal coordinates to Cartesian coordinates was discussed before.1 The use of rotation matrices was found to be slightly more efficient than that of quaternion although quaternion operators have been widely advertised for rotational operations, especially in molecular dynamics simulations of liquids where the orientation is a dynamical variable.2 The discussion on computational efficiency is extended here to a more general case in which bond angles and sidechain torsion angles are allowed to vary. The algorithm of Thompson3 is derived again in terms of quaternions as well as rotation matrices, and an algorithm with optimal efficiency is described. The algorithm based on rotation matrices is again found to be slightly more efficient than that based on quaternions.
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Efficiency of Rotational Operators for Geometric Manipulation of Chain Molecules
Chaok Seok*,Evangelos A. Coutsias* 대한화학회 2007 Bulletin of the Korean Chemical Society Vol.28 No.10
Geometric manipulation of molecules is an essential elementary component in computational modeling programs for molecular structure, stability, dynamics, and design. The computational complexity of transformation of internal coordinates to Cartesian coordinates was discussed before.1 The use of rotation matrices was found to be slightly more efficient than that of quaternion although quaternion operators have been widely advertised for rotational operations, especially in molecular dynamics simulations of liquids where the orientation is a dynamical variable.2 The discussion on computational efficiency is extended here to a more general case in which bond angles and sidechain torsion angles are allowed to vary. The algorithm of Thompson3 is derived again in terms of quaternions as well as rotation matrices, and an algorithm with optimal efficiency is described. The algorithm based on rotation matrices is again found to be slightly more efficient than that based on quaternions.
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The FALC-Loop web server for protein loop modeling
Ko, Junsu,Lee, Dongseon,Park, Hahnbeom,Coutsias, Evangelos A.,Lee, Julian,Seok, Chaok Oxford University Press 2011 Nucleic acids research Vol.39 No.2
<P>The FALC-Loop web server provides an online interface for protein loop modeling by employing an <I>ab initio</I> loop modeling method called FALC (fragment assembly and analytical loop closure). The server may be used to construct loop regions in homology modeling, to refine unreliable loop regions in experimental structures or to model segments of designed sequences. The FALC method is computationally less expensive than typical <I>ab initio</I> methods because the conformational search space is effectively reduced by the use of fragments derived from a structure database. The analytical loop closure algorithm allows efficient search for loop conformations that fit into the protein framework starting from the fragment-assembled structures. The FALC method shows prediction accuracy comparable to other state-of-the-art loop modeling methods. Top-ranked model structures can be visualized on the web server, and an ensemble of loop structures can be downloaded for further analysis. The web server can be freely accessed at http://falc-loop.seoklab.org/.</P>
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Protein loop modeling by using fragment assembly and analytical loop closure
Lee, Julian,Lee, Dongseon,Park, Hahnbeom,Coutsias, Evangelos A.,Seok, Chaok Wiley Subscription Services, Inc., A Wiley Company 2010 Proteins Vol.78 No.16
<P><B>Abstract</B></P><P>Protein loops are often involved in important biological functions such as molecular recognition, signal transduction, or enzymatic action. The three dimensional structures of loops can provide essential information for understanding molecular mechanisms behind protein functions. In this article, we develop a novel method for protein loop modeling, where the loop conformations are generated by fragment assembly and analytical loop closure. The fragment assembly method reduces the conformational space drastically, and the analytical loop closure method finds the geometrically consistent loop conformations efficiently. We also derive an analytic formula for the gradient of any analytical function of dihedral angles in the space of closed loops. The gradient can be used to optimize various restraints derived from experiments or databases, for example restraints for preferential interactions between specific residues or for preferred backbone angles. We demonstrate that the current loop modeling method outperforms previous methods that employ residue‐based torsion angle maps or different loop closure strategies when tested on two sets of loop targets of lengths ranging from 4 to 12. Proteins 2010. © 2010 Wiley‐Liss, Inc.</P>
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