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## Dynamic Programming and Clique Based Approaches for Protein Threading with Profiles and Constraints ∗ (2006)

### Citations

8556 | Gapped BLAST and PSIBLAST: a new generation of protein database search programs
- Altschul, Madden, et al.
- 1997
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Citation Context ... threading with position specific score matrices) is also known as a powerful method for structure prediction. In particular, PSIBLAST is widely used both for homology search and structure prediction =-=[6]-=-. Thus, it is reasonable to try to develop algorithms for protein threading with profiles and constraints, which may be useful to improve the prediction accuracy by PSI-BLAST. In this paper, we theref... |

1386 | The Protein Data Bank
- Berman
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Citation Context ...6 The Institute of Electronics, Information and Communication Engineerss1216 based on our previous work [7]. We perform computational experiments on both algorithms using PDB (Protein Data Bank) data =-=[11]-=-. The results suggest that constraints are useful to improve the prediction accuracy of protein threading. That is, constraints are useful to improve the quality of alignments between sequences and st... |

1278 |
Approximation Algorithms
- Vazirani
- 2003
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Citation Context ...(n+2)+1+h)| h < k, {vh,vk} ∈E}. Then, it is easy to see that there exists a feasible threading if and only if there exists a clique of size K. � Next we study approximation hardness of Problem 2 (see =-=[25]-=- for terminologies on approximation algorithms). For that purpose, we assume that PFt takes non-negative values. We also need the following lemma. Lemma 1: Let G(V, E) be an undirected graph where eac... |

747 | The SWISS-PROT protein knowledgebase and its supplement TrEMBL in 2003 - Boeckmann, Bairoch, et al. - 2003 |

303 |
Computers and Intractability
- Garey, Johnson
- 1979
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Citation Context ...s with arc annotations [14]–[16]. Proposition 1: Both Problem 2 and Problem 3 are NPhard. Proof: We reduce the decision version of maximum clique, where maximum clique is a well-known NP-hard problem =-=[23]-=-, [24]. Let G(V, E) be an undirected graph where V = {v1,...,vn}, and suppose that we are asked whether or not there exists a clique (i.e., a complete subgraph) V ′ ⊆ V of size K. From that instance, ... |

160 |
Clique is hard to approximate within n 1−ɛ
- Hastad
- 1999
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Citation Context ... arc annotations [14]–[16]. Proposition 1: Both Problem 2 and Problem 3 are NPhard. Proof: We reduce the decision version of maximum clique, where maximum clique is a well-known NP-hard problem [23], =-=[24]-=-. Let G(V, E) be an undirected graph where V = {v1,...,vn}, and suppose that we are asked whether or not there exists a clique (i.e., a complete subgraph) V ′ ⊆ V of size K. From that instance, we con... |

122 | The protein threading problem with sequence amino acid interaction preferences is NP-complete. - Lathrop - 1994 |

92 |
RAPTOR: optimal protein threading by linear programming.
- Xu, Li, et al.
- 2003
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Citation Context ..., while arcs for template sequences were considered in [7]. Using this property and treating each residue in As as a core region, most exact algorithms for protein threading with pairwise energy [1], =-=[19]-=-, [20] might be modified for protein threading with profiles and constraints in which gaps are allowed everywhere (note that gaps are not allowed in core regions if simple modifications are done for t... |

88 | K.: A general edit distance between RNA structures
- Jiang, Lin, et al.
- 2002
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Citation Context ...ctions between core regions has a tree-like (nested) structure. Jiang et al. developed similar algorithms for special cases of the longest common subsequence problem for arc annotated sequences [14], =-=[15]-=-. In this section, we develop a similar DP algorithm for a special case of Problem 2 and then combine it with a branch-and-bound procedure for a general case. We consider a special case in which any t... |

69 | Global optimum protein threading with gapped alignment and empirical pair score functions.
- Lathrop, Smith
- 1996
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Citation Context ...lique based algorithm CLIQUETHREAD and the DP based algorithm BBDPTHREAD. From a practical viewpoint, it seems that most exact algorithms for protein threading with pairwise contact energy [1], [19], =-=[20]-=- can be modified for threading with constraints as in [1]. However, gaps in core regions are not allowed in these algorithms whereas gaps are allowed in our algorithms. At least, our algorithms are si... |

58 |
High throughput protein fold identification by using experimental constraints derived from intramolecular cross-links and mass spectrometry.
- Young, Tang, et al.
- 2000
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Citation Context ...l. recently developed a novel experimental method to aid in construction of a homology model by using chemical cross-linking and time-of-flight (TOF) mass spectrometry to identify LYS-LYS cross-links =-=[5]-=-. Instead of X-ray crystallography and NMR that require much amount Manuscript received August 13, 2005. Manuscript revised November 2, 2005. Final manuscript received December 15, 2005. † The authors... |

58 | C.H.: Algorithmic aspects of protein structure similarity. In:
- Goldman, Istrail, et al.
- 1999
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Citation Context ...pairwise contact energy [7]. As discussed in Sect. 6, threading with profiles and constraints is very similar to that problem. Goldman et al. studied theoretical aspect of protein structure alignment =-=[12]-=-. Recently, the longest common subsequence problem with arc annotations is extensively studied [13]–[16]. Though these studies have been done independently, similar results were obtained. However, it ... |

52 |
An efficient branch-and-bound algorithm for finding a maximum clique with computational experiments.
- Tomita, Kameda
- 2007
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Citation Context ...DPTHREAD. CLIQUETHREAD reduces constrained threading to the maximum edge weight clique problem. Though the maximum clique is NP-hard, several practically efficient algorithms have been developed [9], =-=[10]-=-. BBDPTHREAD combines a DP (dynamic programming) algorithm and a branch-andbound procedure, where the DP algorithm is developed Copyright c○ 2006 The Institute of Electronics, Information and Communic... |

52 | 101 optimal PDB structure alignments: A Branch-and-cut algorithm for the maximum contact map overlap problem. In:
- Lancia, Carr, et al.
- 2001
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Citation Context ...h the total weight for edges in the clique is maximized under the condition that the number of vertices of the clique is maximum. Though clique-based approach was also studied for structure alignment =-=[26]-=-, existing methods can not be directly applied to our problem because affine gap costs and profiles are considered in this paper whereas they solved the structure alignment problem in discrete setting... |

38 |
Finding common subsequences with arcs and pseudoknots,
- Evans
- 1999
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Citation Context ...ry similar to that problem. Goldman et al. studied theoretical aspect of protein structure alignment [12]. Recently, the longest common subsequence problem with arc annotations is extensively studied =-=[13]-=-–[16]. Though these studies have been done independently, similar results were obtained. However, it should be pointed out that our previous work [7] is one of the earliest work. Although, the authors... |

37 |
The longest common subsequence problem for sequences with nested arc annotations,
- Lin, Chen, et al.
(Show Context)
Citation Context ...milar to that problem. Goldman et al. studied theoretical aspect of protein structure alignment [12]. Recently, the longest common subsequence problem with arc annotations is extensively studied [13]–=-=[16]-=-. Though these studies have been done independently, similar results were obtained. However, it should be pointed out that our previous work [7] is one of the earliest work. Although, the authors have... |

26 |
Rapid protein fold determination using unassigned NMR data. Proc Natl Acad Sci USA
- Meiler, Baker
- 2003
(Show Context)
Citation Context ...tion of the protein threading [2]. An algorithm using unassigned NMR data that relies on ROSETTA and a Monte Carlo procedure for the generation of low resolution protein structures has been developed =-=[3]-=-. Moreover, methods like TOUCHSTONEX [4] have been proposed that incorporates a limited number of distance restraints into the force field as NOE-specific pairwise interaction to predict protein struc... |

23 | Protein structure alignment using dynamic programming and iterative improvement
- Akutsu
- 1996
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Citation Context ... similarity between the two compared structures. We also listed the results of structural alignment for the evaluation. We employed STRALIGN (http://www.hgc.ims.utokyo.ac.jp/service/tooldoc/stralign) =-=[27]-=- for structure alignment, where it was developed by the authors and its performance was considered to be comparable to other structure alignment algorithms. It should be noted that complete structural... |

9 |
A computational method for NMRconstrained protein threading
- Xu, Xu, et al.
- 2000
(Show Context)
Citation Context ...eved by the significant utilization of distance restraints. Xu et al. showed that (partial) information obtained from NMR experiments is useful to improve the accuracy of the protein threading method =-=[1]-=-, where protein threading is one of the powerful computational approaches to protein structure prediction. Young et al. recently developed a novel experimental method to aid in construction of a homol... |

6 |
Constraint-based assembly of tertiary protein structures from secondary structure elements. Protein Sci 9:1935--1946
- Yue, Dill
- 2000
(Show Context)
Citation Context ...y experiments on fold recognition, are important future work, too. Though we considered the threading approach for structure prediction with constraints, the ab-initio approach should also be studied =-=[28]-=-. It is interesting that Propositions 1 and 2, and the DP algorithm used in BBDPTHREAD are similar to our previous results on protein threading with pairwise energy [7] though the roles of a target se... |

5 | Improving fold recognition of protein threading by experimental distance constraints
- Albrecht, Hanisch, et al.
(Show Context)
Citation Context ...the PROSPECT algorithm for protein threading with pairwise contact energy and constraints [1]. Another algorithm was also proposed for the improvement in the fold recognition of the protein threading =-=[2]-=-. An algorithm using unassigned NMR data that relies on ROSETTA and a Monte Carlo procedure for the generation of low resolution protein structures has been developed [3]. Moreover, methods like TOUCH... |

4 |
An algorithm for finding a maximum clique with maximum edge-weight and computational experiments
- Suzuki, Tomita, et al.
- 2002
(Show Context)
Citation Context ...nd BBDPTHREAD. CLIQUETHREAD reduces constrained threading to the maximum edge weight clique problem. Though the maximum clique is NP-hard, several practically efficient algorithms have been developed =-=[9]-=-, [10]. BBDPTHREAD combines a DP (dynamic programming) algorithm and a branch-andbound procedure, where the DP algorithm is developed Copyright c○ 2006 The Institute of Electronics, Information and Co... |

4 |
The Longest Common Subsequence Problem with Crossing-Free Arc-Annotated Sequences
- Blin, Jiang, et al.
(Show Context)
Citation Context .... (si, si ′) ∈ As and (t j, t j ′) � At. It should be noted that IC is uniquely determined from As and At. Similar constraints are used in the longest common subsequence problems with arc annotations =-=[14]-=-–[16]. Proposition 1: Both Problem 2 and Problem 3 are NPhard. Proof: We reduce the decision version of maximum clique, where maximum clique is a well-known NP-hard problem [23], [24]. Let G(V, E) be ... |

2 |
Protein threading with profiles and distance constraints using clique based algorithms,
- Bahadur, Tomita, et al.
- 2006
(Show Context)
Citation Context ...revious work [7] is one of the earliest work. Although, the authors have already presented the improved version of the clique based algorithm for protein threading with profiles and constraints [17], =-=[18]-=-, only this paper deals with the theoretical analysis of the problem, and the dynamic programming based algorithm, BBDPTHREAD. Furthermore, the clique based algorithm is also initially presented in th... |

1 |
TOUCHSTONEX: Protein structure prediction with sparse NMR data,” Proteins: Struct
- Kihara, Huang, et al.
- 2003
(Show Context)
Citation Context ...gorithm using unassigned NMR data that relies on ROSETTA and a Monte Carlo procedure for the generation of low resolution protein structures has been developed [3]. Moreover, methods like TOUCHSTONEX =-=[4]-=- have been proposed that incorporates a limited number of distance restraints into the force field as NOE-specific pairwise interaction to predict protein structures at low-medium resolution. However,... |

1 |
On the approximation of protein threading,” Theor
- Akutsu, Miyano
- 1999
(Show Context)
Citation Context ...periments) is NP-hard. Moreover, we show a strong hardness result on the approximation of an optimal feasible threading. It should be noted that protein threading with pair score functions is NP-hard =-=[7]-=-, [8], whereas protein threading with profiles can be solved efficiently using dynamic programming as in sequence alignment. Our results show that adding constraints makes the problem much harder. Fur... |

1 | Clique based algorithms for protein threading with profiles and constraints
- C, Tomita, et al.
- 2005
(Show Context)
Citation Context ... our previous work [7] is one of the earliest work. Although, the authors have already presented the improved version of the clique based algorithm for protein threading with profiles and constraints =-=[17]-=-, [18], only this paper deals with the theoretical analysis of the problem, and the dynamic programming based algorithm, BBDPTHREAD. Furthermore, the clique based algorithm is also initially presented... |