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## Rapid protein side-chain packing via tree decomposition (2005)

Venue: | Research in Computational Molecular Biology, Lecture Notes in Computer Science |

Citations: | 26 - 1 self |

### Citations

1566 |
Comparative protein modelling by satisfaction of spatial restraints.
- Sali, TL
- 1993
(Show Context)
Citation Context ... side-chain atoms simultaneously. The side-chain prediction problem has been proved to be NP-hard [29, 30], which justifies the development of many heuristic algorithms such as SCAP [19] and MODELLER =-=[31]-=-, and some approximate algorithms [23, 24]. These algorithms are usually computationally efficient, but cannot guarantee to find the side-chain assignment with the lowest system energy. The exact algo... |

984 | An optimal algorithm for approximate nearest neighbor searching in fixed dimensions”,
- Arya, Mount, et al.
- 1998
(Show Context)
Citation Context ...ruct the residue interaction graph according to its definition described in Section 2. We build SCATD using BALL library [40] for some basic objects such as proteins, residues, and atoms, ANN library =-=[41, 42]-=- to determine if two atoms conflict or not, and split package [43] for tree decomposition of a graph. 5.1 Computational Efficiency The residue interaction graphs are decomposed into small components w... |

441 |
Graph minors II. Algorithmic aspects of tree-width.
- Robertson, Seymour
- 1986
(Show Context)
Citation Context ...an efficient heuristic algorithm to find a good tree decomposition of a graph. 3.1 Tree Decomposition Concepts The notions of tree width and tree decomposition are introduced by Robertson and Seymour =-=[34]-=- in their work on graph minors. The tree decomposition of a sparse graph has been applied to many NP-hard problems such as frequency assignment problem [35] and Bayesian inference [36]. Definition 1. ... |

386 | Complexity of finding embeddings in a k-tree.
- Arnborg, Corneil, et al.
- 1987
(Show Context)
Citation Context ...need an algorithm to decompose the interaction graph into very small components. 3.3 Construction of Tree Decomposition The optimal tree decomposition of a general graph has been proved to be NP-hard =-=[37]-=-, which means it is unlikely to find the optimal decomposition of a graph within polynomial time. However, since the residue interaction graph is a geometric graph, we can very quickly obtain a tree d... |

280 |
Enhanced genome annotation using structural profiles in the program 3D-PSSM.
- Kelley, MacCallum, et al.
- 2000
(Show Context)
Citation Context ...ee two, we can prune it by modifying the pairwise interaction scores of its two adjacent residues j1, j2 as follows. Pj1,j2(k1, k2) ← Pj1,j2(k1, k2) + min l∈D[i] {Si(l) + Pi,j1(l, k1) + Pi,j2(l, k2)} =-=(5)-=- Since residue i only interacts with two residues j1 and j2, for each combination of rotamer assignment to j1 and j2, we can find the best rotamer for i and then remove i from the system. The optimal ... |

258 | ANN: A Library for Approximate Nearest Neighbor Searching.
- Mount, Arya
- 2010
(Show Context)
Citation Context ...ruct the residue interaction graph according to its definition described in Section 2. We build SCATD using BALL library [40] for some basic objects such as proteins, residues, and atoms, ANN library =-=[41, 42]-=- to determine if two atoms conflict or not, and split package [43] for tree decomposition of a graph. 5.1 Computational Efficiency The residue interaction graphs are decomposed into small components w... |

222 |
FUGUE: Sequence-structure homology recognition using environment-specific substitution tables and structure-dependent gap penalties.
- Shi, Blundell, et al.
- 2001
(Show Context)
Citation Context ...wo major steps. One is the prediction of the backbone atom coordinates and the other is the prediction of side-chain atom coordinates. The former step is usually done using protein threading programs =-=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]-=- or sequence-based homology search tools such as PDB-BLAST [11]. The task of side-chain prediction is to determine the position of all the side-chain atoms given that the backbone coordinates of a pro... |

214 | GenTHREADER: an efficient and reliable protein fold recognition method for genomics sequences.
- Jones
- 1999
(Show Context)
Citation Context ...ystem. For a residue i with degree one, assume i is only adjacent to residue j. Then, we can remove i by modifying the singleton score of j as follows. Sj(k) ← Sj(k) + min l∈D[i] {Si(l) + Pi,j(l, k)} =-=(4)-=- Since residue i only interacts with residue j, for each rotamer k of residue j, we can find the best rotamer for residue i and then remove residue i from the system. The optimal system energy will no... |

107 |
Lasters I: The dead-end elimination theorem and its use in protein side-chain positioning. Nature
- Desmet, Maeyer, et al.
- 1992
(Show Context)
Citation Context ...algorithms [23, 24]. These algorithms are usually computationally efficient, but cannot guarantee to find the side-chain assignment with the lowest system energy. The exact algorithms such as DEE/A ∗ =-=[14, 32]-=- and integer programming approach [25, 27] can find a globally minimum energy for a given rotamer library and an energy function. However, not many algorithms belong to this category due to the expens... |

107 | A graph-theory algorithm for rapid protein side-chain prediction,”
- Canutescu, Shelenkov, et al.
- 2003
(Show Context)
Citation Context ...[25, 27] can find a globally minimum energy for a given rotamer library and an energy function. However, not many algorithms belong to this category due to the expensive computational time. SCWRL 3.0 =-=[17]-=- guarantees to find a globally optimal solution and also runs very fast for many proteins. SCWRL 3.0 first decomposes the residue interaction graph into some small biconnected components. Any two bico... |

100 | Separators for spherepackings and nearest neighbor graphs.
- Miller, Teng, et al.
- 1997
(Show Context)
Citation Context ...me. However, since the residue interaction graph is a geometric graph, we can very quickly obtain a tree decomposition with width O(|V | 2 3 log |V |), based on the following sphere separator theorem =-=[38]-=-. Theorem 1. Given a residue interaction graph G = (V, E), there is a separator subset U with size O(|V | 2 3) of V such that removal of U from the graph can partition V into two subsets V1 and V2, an... |

92 |
RAPTOR: optimal protein threading by linear programming.
- Xu, Li, et al.
- 2003
(Show Context)
Citation Context ...algorithms to the problem. With aspolynomial-time algorithm, we can deal with a larger rotamer library, which may result in a better prediction accuracy. In protein structure prediction server RAPTOR =-=[44, 45]-=-, we have developed a linear programming (LP) algorithm to obtain the globally optimal solution of the protein threading problem. The LP formulation used by RAPTOR can also be used to formulate the si... |

89 | E!cient approximation for triangulation of minimum treewidth,
- Amir
- 2001
(Show Context)
Citation Context ...ed in Section 2. We build SCATD using BALL library [40] for some basic objects such as proteins, residues, and atoms, ANN library [41, 42] to determine if two atoms conflict or not, and split package =-=[43]-=- for tree decomposition of a graph. 5.1 Computational Efficiency The residue interaction graphs are decomposed into small components with size no more than 10, much smaller than that reported in SCWRL... |

89 |
Prediction of protein side-chain rotamers from a backbone-dependent rotamer library: a new homology modeling tool.
- Bower, Cohen, et al.
- 1997
(Show Context)
Citation Context ...ction is becoming more important since the backbone coordinates of a protein can be predicted accurately. Many side-chain prediction methods have been proposed and implemented in the past two decades =-=[12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]-=-. Almost all of them use a rotamer library, which is a set of side-chain conformation candidates. In order to overcome computational difficulty, the side-chain conformation of a residue is discretized... |

81 |
Extending the accuracy limits of prediction for side-chain conformations.
- Xiang, Honig
- 2001
(Show Context)
Citation Context ...ll the interacting side-chain atoms simultaneously. The side-chain prediction problem has been proved to be NP-hard [29, 30], which justifies the development of many heuristic algorithms such as SCAP =-=[19]-=- and MODELLER [31], and some approximate algorithms [23, 24]. These algorithms are usually computationally efficient, but cannot guarantee to find the side-chain assignment with the lowest system ener... |

80 |
Database algorithm for generating protein backbone and side-chain coordinates from C-trace
- Holm, Sander
- 1991
(Show Context)
Citation Context ...ction is becoming more important since the backbone coordinates of a protein can be predicted accurately. Many side-chain prediction methods have been proposed and implemented in the past two decades =-=[12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]-=-. Almost all of them use a rotamer library, which is a set of side-chain conformation candidates. In order to overcome computational difficulty, the side-chain conformation of a residue is discretized... |

64 |
Efficient rotamer elimination applied to protein side-chains and related spin-glasses.
- Goldstein
- 1994
(Show Context)
Citation Context ...sidue interaction graph can be decomposed into components of 4 or 5 residues using our decomposition method. Since each residue has no more than 4 candidate rotamers after the Goldstein criterion DEE =-=[33]-=- is conducted, the optimal sidechain assignment of each component can be done very quickly. The remainder of this paper is organized as follows. In Section 2, we describe the side-chain assignment pro... |

64 | Thin junction trees.
- Bach, Jordan
- 2001
(Show Context)
Citation Context ...son and Seymour [34] in their work on graph minors. The tree decomposition of a sparse graph has been applied to many NP-hard problems such as frequency assignment problem [35] and Bayesian inference =-=[36]-=-. Definition 1. Let G = (V, E) be a graph. A tree decomposition of G is a pair (T, X) satisfying the following conditions:s1. T = (I, F) is a tree with a node set I and an edge set F , 2. X = {Xi|i ∈ ... |

63 |
Backbone-dependent rotamer library for proteins. Application to side-chain prediction.
- Karplus
- 1993
(Show Context)
Citation Context ...depends on two dihedral angles (φ and ψ) associated with the residue. For example, Dunbrack et al. first developed a backbone-independent rotamer library and then a backbone-dependent rotamer library =-=[28]-=-. Given a rotamer library, the side-chain prediction problem can be formulated as a combinatorial search problem. The quality of a side-chain packing can be measured by an energy function, which usual... |

44 | Protein design is NP-hard
- Pierce, Winfree
- 2002
(Show Context)
Citation Context ... reason is that in order to minimize the conflict, we have to fix the positions of all the interacting side-chain atoms simultaneously. The side-chain prediction problem has been proved to be NP-hard =-=[29, 30]-=-, which justifies the development of many heuristic algorithms such as SCAP [19] and MODELLER [31], and some approximate algorithms [23, 24]. These algorithms are usually computationally efficient, bu... |

43 |
TOPITS: threading one-dimensional predictions into three-dimensional structures.
- Rost
- 1995
(Show Context)
Citation Context ...wo angles φ and ψ. Then we calculate Si(l) and Pi,j(l, k) as follows [17]. Pri(l|φ, ψ) � Si(l) = −K log( ) + maxl∈D[i] Pri(l|φ, ψ) Pi,j(l, k) = � � a∈SC(i) b∈SC(j) � � |i−j|>1 s∈SC(i) b∈BB(j) E(s, b) =-=(1)-=- E(a, b) (2) In Eq. 1, K is optimized to 6 to yield the best prediction accuracy. Please notice that in the above two equations, the position of one side-chain atom depends on its associated rotamer. ... |

39 | Fast protein fold recognition via sequence to structure alignment and contact capacity potentials. Pacific Symposium on Biocomputing ‘96
- NN, Nussinov, et al.
- 1995
(Show Context)
Citation Context ...wo major steps. One is the prediction of the backbone atom coordinates and the other is the prediction of side-chain atom coordinates. The former step is usually done using protein threading programs =-=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]-=- or sequence-based homology search tools such as PDB-BLAST [11]. The task of side-chain prediction is to determine the position of all the side-chain atoms given that the backbone coordinates of a pro... |

37 |
Arby: automatic protein structure prediction using profile-profile alignment and confidence measures
- Ohsen, Sommer, et al.
- 2004
(Show Context)
Citation Context ...wo major steps. One is the prediction of the backbone atom coordinates and the other is the prediction of side-chain atom coordinates. The former step is usually done using protein threading programs =-=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]-=- or sequence-based homology search tools such as PDB-BLAST [11]. The task of side-chain prediction is to determine the position of all the side-chain atoms given that the backbone coordinates of a pro... |

37 | Solving and analyzing side-chain positioning problems using linear and integer programming
- Kingsford, Chazelle, et al.
(Show Context)
Citation Context ...side-chain prediction problem has been proved to be NP-hard [29, 30], which justifies the development of many heuristic algorithms such as SCAP [19] and MODELLER [31], and some approximate algorithms =-=[23, 24]-=-. These algorithms are usually computationally efficient, but cannot guarantee to find the side-chain assignment with the lowest system energy. The exact algorithms such as DEE/A ∗ [14, 32] and intege... |

36 |
An efficient computational method for globally optimal threading”,
- Xu, Xu, et al.
- 1998
(Show Context)
Citation Context ...and ψ. Then we calculate Si(l) and Pi,j(l, k) as follows [17]. Pri(l|φ, ψ) � Si(l) = −K log( ) + maxl∈D[i] Pri(l|φ, ψ) Pi,j(l, k) = � � a∈SC(i) b∈SC(j) � � |i−j|>1 s∈SC(i) b∈BB(j) E(s, b) (1) E(a, b) =-=(2)-=- In Eq. 1, K is optimized to 6 to yield the best prediction accuracy. Please notice that in the above two equations, the position of one side-chain atom depends on its associated rotamer. Given a side... |

32 |
Fast and accurate side-chain topology and energy refinement (FASTER) as a new method for protein structure optimization
- Desmet, Spriet, et al.
(Show Context)
Citation Context ...ction is becoming more important since the backbone coordinates of a protein can be predicted accurately. Many side-chain prediction methods have been proposed and implemented in the past two decades =-=[12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]-=-. Almost all of them use a rotamer library, which is a set of side-chain conformation candidates. In order to overcome computational difficulty, the side-chain conformation of a residue is discretized... |

32 | Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm. Proteins
- Leach, Lemon
- 1998
(Show Context)
Citation Context ... algorithms [23, 24]. These algorithms are usually computationally efficient, but cannot guarantee to find the side-chain assignment with the lowest system energy. The exact algorithms such as DEE/A∗ =-=[14, 32]-=- and integer programming approach [25, 27] can find a globally minimum energy for a given rotamer library and an energy function. However, not many algorithms belong to this category due to the expens... |

30 | On the approximation of protein threading.
- Akutsu, Miyano
- 1999
(Show Context)
Citation Context |

28 | A semidefinite programming approach to side chain positioning with new rounding strategies
- Chazelle, Kingsford, et al.
(Show Context)
Citation Context ...side-chain prediction problem has been proved to be NP-hard [29, 30], which justifies the development of many heuristic algorithms such as SCAP [19] and MODELLER [31], and some approximate algorithms =-=[23, 24]-=-. These algorithms are usually computationally efficient, but cannot guarantee to find the side-chain assignment with the lowest system energy. The exact algorithms such as DEE/A ∗ [14, 32] and intege... |

26 | The minimum degree heuristic and the minimal triangulation process.
- Berry, Heggernes, et al.
- 2003
(Show Context)
Citation Context ...ristic algorithm are good enough. Many of them have a tree width of only 3 or 4, which leads to a very efficient algorithm for side-chain prediction. In our program, we use “minimum degree” heuristic =-=[39]-=- to recursively partition the graph. Specifically, we choose the vertex with the smallest number of neighbors. Then we add edges to the graph such that any two neighbors of the selected vertex is conn... |

25 |
Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm.
- AR, AP
- 1998
(Show Context)
Citation Context ...algorithms [23, 24]. These algorithms are usually computationally efficient, but cannot guarantee to find the side-chain assignment with the lowest system energy. The exact algorithms such as DEE/A ∗ =-=[14, 32]-=- and integer programming approach [25, 27] can find a globally minimum energy for a given rotamer library and an energy function. However, not many algorithms belong to this category due to the expens... |

23 |
BALL--rapid software prototyping in computational molecular biology. Biochemicals Algorithms Library,"
- Kohlbacher, Lenhof
- 2000
(Show Context)
Citation Context .... Finally, we Rapid Protein Side-Chain Packing via Tree Decomposition 433 construct the residue interaction graph according to its definition described in Section 2. We build SCATD using BALL library =-=[40]-=- for some basic objects such as proteins, residues, and atoms, ANN library [41, 42] to determine if two atoms conflict or not, and split package [43] for tree decomposition of a graph. 5.1 Computation... |

19 |
A branch-andbound algorithm for optimal protein threading with pairwise (contact potential) amino acid interactions.
- Lathrop, Smith
- 1994
(Show Context)
Citation Context |

19 | Protein threading by linear programming
- Xu, Li, et al.
- 2003
(Show Context)
Citation Context ...algorithms to the problem. With aspolynomial-time algorithm, we can deal with a larger rotamer library, which may result in a better prediction accuracy. In protein structure prediction server RAPTOR =-=[44, 45]-=-, we have developed a linear programming (LP) algorithm to obtain the globally optimal solution of the protein threading problem. The LP formulation used by RAPTOR can also be used to formulate the si... |

18 |
Sidechain modeling with an optimized scoring function. Prot Sci 2002;11:322–331
- Liang, Grishin
(Show Context)
Citation Context |

17 | Determinants of side chain conformational preferences in protein structures - Samudrala, Moult - 1998 |

15 | Side chain-positioning as an integer programming problem
- Eriksson, Zhou, et al.
(Show Context)
Citation Context ...usually computationally efficient, but cannot guarantee to find the side-chain assignment with the lowest system energy. The exact algorithms such as DEE/A ∗ [14, 32] and integer programming approach =-=[25, 27]-=- can find a globally minimum energy for a given rotamer library and an energy function. However, not many algorithms belong to this category due to the expensive computational time. SCWRL 3.0 [17] gua... |

13 | NP-hardness results for protein side-chain packing
- Akutsu
- 1997
(Show Context)
Citation Context ... reason is that in order to minimize the conflict, we have to fix the positions of all the interacting side-chain atoms simultaneously. The side-chain prediction problem has been proved to be NP-hard =-=[29, 30]-=-, which justifies the development of many heuristic algorithms such as SCAP [19] and MODELLER [31], and some approximate algorithms [23, 24]. These algorithms are usually computationally efficient, bu... |

12 |
Construction of side-chains in homology modelling. Application to the C-terminal lobe of rhizopuspepsin.
- Summers, Karplus
- 1989
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Citation Context |

12 |
Solving frequency assignment problems via tree-decomposition
- Koster, Hoesel, et al.
- 1999
(Show Context)
Citation Context ...ion are introduced by Robertson and Seymour [34] in their work on graph minors. The tree decomposition of a sparse graph has been applied to many NP-hard problems such as frequency assignment problem =-=[35]-=- and Bayesian inference [36]. Definition 1. Let G = (V, E) be a graph. A tree decomposition of G is a pair (T, X) satisfying the following conditions:s1. T = (I, F) is a tree with a node set I and an ... |

11 |
Protein structure prediction method for genome-scale applications
- Kim, Xu, et al.
(Show Context)
Citation Context ... a side-chain assignment A(i) ∈ D[i] to residue i (i ∈ V ), the quality of one side-chain packing is measured by the following energy function. E(G) = � Si(A(i)) + � i∈V i�=j,(i,j)∈E Pi,j(A(i), A(j)) =-=(3)-=- The smaller the system energy E(G) is, the better the side-chain assignment. So our goal is to develop an efficient algorithm to search for the side-chain assignment such that the energy E(G) in Eq. ... |

8 |
Comparative modeling of CASP3 targets using
- Jr
- 1999
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Citation Context |

5 | Dunbrack Jr. Prediction of protein side-chain rotamers from a backbone-dependent rotamer library: A new homology modeling tool - Bower, Cohen, et al. - 1997 |

5 |
T.: Protein side-chain packing problem: a maximum common edge-weight clique algorithmic approach. In: The Second Asia Pacific Bioinformatics Conference
- Dukka, Tomita, et al.
- 2004
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Citation Context |

4 |
A.: Saturated BLAST: detecting distant homology using automated multiple intermediate sequence BLAST search. Bioinformatics 16
- Li, Pio, et al.
- 2000
(Show Context)
Citation Context ...nates and the other is the prediction of side-chain atom coordinates. The former step is usually done using protein threading programs [1–10] or sequence-based homology search tools such as PDB-BLAST =-=[11]-=-. The task of side-chain prediction is to determine the position of all the sidechain atoms given that the backbone coordinates of a protein are already known. Along with the advancement of protein ba... |

4 |
rapid software prototyping in computational molecular biology. Bioinformatics
- BALL
- 2000
(Show Context)
Citation Context ...s that cannot be a part of the optimal side-chain assignment. Finally, we construct the residue interaction graph according to its definition described in Section 2. We build SCATD using BALL library =-=[40]-=- for some basic objects such as proteins, residues, and atoms, ANN library [41, 42] to determine if two atoms conflict or not, and split package [43] for tree decomposition of a graph. 5.1 Computation... |

4 |
E.: Protein design is NP-hard. Protein Engineering 15
- Pierce, Winfree
- 2002
(Show Context)
Citation Context ... reason is that in order to minimize the conflict, we have to fix the positions of all the interacting side-chain atoms simultaneously. The side-chain prediction problem has been proved to be NP-hard =-=[29, 30]-=-, which justifies the development of many heuristic algorithms such as SCAP [19] and MODELLER [31], and some approximate algorithms [23, 24]. These algorithms are usually computationally efficient, bu... |

1 | Protein side-chain placement: probabilistic inference and integer programming methods
- Hong, Lozano-Perez
- 2004
(Show Context)
Citation Context |

1 |
A branch and cut algorithm for the optimal solution of the side-chain placement problem
- Althaus, Kohlbacher, et al.
- 2000
(Show Context)
Citation Context ...usually computationally efficient, but cannot guarantee to find the side-chain assignment with the lowest system energy. The exact algorithms such as DEE/A ∗ [14, 32] and integer programming approach =-=[25, 27]-=- can find a globally minimum energy for a given rotamer library and an energy function. However, not many algorithms belong to this category due to the expensive computational time. SCWRL 3.0 [17] gua... |