## On the Approximation of Protein Threading (1997)

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Venue: | Theoretical Computer Science |

Citations: | 29 - 2 self |

### BibTeX

@ARTICLE{Akutsu97onthe,

author = {Tatsuya Akutsu and Satoru Miyano},

title = {On the Approximation of Protein Threading},

journal = {Theoretical Computer Science},

year = {1997},

volume = {210},

pages = {261--275}

}

### Years of Citing Articles

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### Abstract

In this paper, we study the protein threading problem, which was proposed for finding a folded 3D protein structure from an amino acid sequence. Since this problem was already proved to be NP-hard by Lathrop, we study polynomial time approximation algorithms. First we show that the protein threading problem is MAX SNP-hard. Next we show that the protein threading problem can be approximated within a factor 4 for a special case in which a graph representing interaction between residues (amino acids) is planar. This case corresponds to a fi-sheet substructure, which appears in most protein structures. 1 Introduction The protein folding problem is, given an amino acid sequence (a string), to find its correctly folded 3D protein structure. It is one of the most important computational problems in molecular biology. Although this problem can be defined as a minimization problem, it is too hard to be solved directly. Recently, an indirect approach called inverse folding was proposed [2, 4,...

### Citations

579 |
Optimization, Approximation, and Complexity Classes
- Papadiitriou, Yannakakis
- 1991
(Show Context)
Citation Context ...OTEIN THREADING is MAX SNPhard even if the maximum vertex degree is bounded by a constant B. From this result, a constant size lower bound of performance ratio follows under the assumption of P 6= NP =-=[1, 13]-=-. Note that the following theorem also gives a much simpler proof of NP-hardness of PROTEIN THREADING than that in [9]. Theorem 3.1 PROTEIN THREADING-B is MAX SNPhard. Proof. We use L-reduction from M... |

373 |
Introduction to Protein Structure
- BrandeĢn, Tooze
- 1991
(Show Context)
Citation Context ...nce between residues exceeds a threshold value [9]. The planar case corresponds to fi-sheet substructure, which appears in most core regions and is known as a kind of secondary structure (see Fig. 2) =-=[3]-=-. fi-sheet consists of multiple fi-strands. To classify fi-sheet structures, topology diagram has been used [3]. In topology diagram, fistarnds are usually arranged parallel in a plane, and each fi-st... |

253 |
A method to identify protein sequences that fold into a known three-dimensional structure
- Bowie, Luthy, et al.
- 1991
(Show Context)
Citation Context ...problems in molecular biology. Although this problem can be defined as a minimization problem, it is too hard to be solved directly. Recently, an indirect approach called inverse folding was proposed =-=[2, 4, 6, 10]-=-. In inverse folding, given an amino acid sequence and a set of protein structures (structural patterns) , a structure into which the sequence is most likely to fold is computed. To test whether or no... |

194 | A new approach to protein fold recognition - Jones, Taylor, et al. - 1992 |

135 |
The complexity of some problems on subsequences and supersequences
- Maier
- 1978
(Show Context)
Citation Context ...IN THREADING-B is NP-hard even if GPT (VPT ; EPT ) is planar. Proof. We use a reduction from the longest common subsequence problem (LCS) over a binary alphabet, which was already shown to be NP-hard =-=[11]-=-. LCS is, given strings s 1 = s 1 1 1 1 1 s 1 n 1 , s 2 = s 2 1 1 1 1 s 2 n 2 , 1 1 1, s k = s k 1 1 1 1 s k n k over 6 0 = f0; 1g and an integer L, to decide whether or not there exists a string s 0 ... |

127 | One thousand families for the molecular biologist - Chothia - 1992 |

97 | The protein threading problem with sequence amino acid interaction preferences is NP-complete
- Lathrop
- 1994
(Show Context)
Citation Context ...corresponding to potential energy) is computed. This minimization problem is called a protein threading problem, and an alignment between a sequence and a structure is called a threading (see Fig. 1) =-=[4, 9, 10]-=-. Note that, in Fig. 1, gaps (insertions and deletions of amino acids) are not allowed in core regions, but allowed only in loop regions, where a protein structure is partitioned into core regions and... |

81 |
An empirical energy function for threading protein sequence through the folding motif
- Bryant, Lawrence
- 1993
(Show Context)
Citation Context ...problems in molecular biology. Although this problem can be defined as a minimization problem, it is too hard to be solved directly. Recently, an indirect approach called inverse folding was proposed =-=[2, 4, 6, 10]-=-. In inverse folding, given an amino acid sequence and a set of protein structures (structural patterns) , a structure into which the sequence is most likely to fold is computed. To test whether or no... |

76 |
N.: Planar Graphs: Theory and Algorithms
- Nishizwki, Chiba
- 1988
(Show Context)
Citation Context ...here t opt denotes an optimal threading. Therefore, the performance ratio of this simple algorithm is at least 4. Since a planar embedding of GPT (VPT ; EPT ) can be computed in O(jVPT j) = O(m) time =-=[12]-=-, we can obtain a partition of EPT into Eu ; E l ; E1 ; E2 in O(m 2 ) time. Therefore, the total computation time is O(mn 4 ) from Lemma 4.1, Lemma 4.2 and msn. ut 5 Concluding Remarks In this paper, ... |

65 | Fast protein folding in the hydrophobic-hydrophilic model within three-eighths of optimal
- Hart, Istrail
- 1996
(Show Context)
Citation Context ...ding up the branch-and-bound procedure. Note that an approximation algorithm has been already developed for the protein folding problem (not the inverse folding problem), but its model was too simple =-=[7]-=-. In this paper, we first show that the protein threading problem is MAX SNP-hard. Moreover, we show that approximation of the problem is at least as hard as approximation of the DENSE-k-SUBGRAPH prob... |

62 | Global optimum protein threading with gapped alignment and empirical pair scoring function - Lathrop, Smith - 1996 |

52 | Embedding graphs in books: a layout problem with applications to VLSI design
- CHUNG, LEIGHTON, et al.
- 1987
(Show Context)
Citation Context ...enotes the number of pairs of cores havingsstrong interactions.sIn approximation algorithms, we use some decompositions of an edge set. Thesesdecompositions are similar to those in the book embedding =-=[7]-=-. However, our decom-spositions are different from those because the ordering of vertices is fixed in our case,swhereas an arbitrary ordering can be selected in the book embedding.s2. The protein thre... |

47 |
On choosing a dense subgraph, in
- Kortsarz, Peleg
- 1993
(Show Context)
Citation Context ...P-hard. Moreover, we show that approximation of the problem is at least as hard as approximation of the DENSE-k-SUBGRAPH problem, for which only an O(n 0:3885 ) ratio approximation algorithm is known =-=[8]-=-. Next we consider a special case in which a graph representing interactions between residues (amino acids) is planar. This case corresponds to most fi-sheet substructures. For this case, we show a po... |

39 |
Sequence-structure matching in globular proteins: application to supersecondary and tertiary structure determination
- Godzik, Skolnick
- 1992
(Show Context)
Citation Context ...problems in molecular biology. Although this problem can be defined as a minimization problem, it is too hard to be solved directly. Recently, an indirect approach called inverse folding was proposed =-=[2, 4, 6, 10]-=-. In inverse folding, given an amino acid sequence and a set of protein structures (structural patterns) , a structure into which the sequence is most likely to fold is computed. To test whether or no... |

31 | Local rules for protein folding on a triangular lattice and generalized hydrophobicity in HP model - Agarwala, Batzoglou, et al. - 1997 |

18 |
A branch-and-bound algorithm for optimal protein threading with pairwise (contact potential) amino acid interactions
- Lathrop, Smith
- 1994
(Show Context)
Citation Context .... Such studies may lead to practical algorithms for protein threading. Although we have not discussed details about score functions, using a good score function is also important in protein threading =-=[10]-=-. However, most of known score functions were not satisfactory from the viewpoint of predictive accuracy if they were applied to the threading problem. Thus, we are currently studying a method for der... |

12 |
complexity classes
- Papadimitriou, Yannakakis, et al.
- 1991
(Show Context)
Citation Context ... were too simple.sIn this paper, we first show that the protein threading problem is MAX SNP-hard,sfrom which a constant size lower bound of performance ratio follows under the as-ssumption of P # NP =-=[2,17]-=-. Moreover, we show a result suggesting that approximationsT. Akutsu, S. Miyanol Theoretical Computer Science 210 (1999) 261-275 263sof the problem is much harder, using an approximation preserving re... |

9 |
A polynomial-time algorithm for a class of protein threading problems
- Xu, Uberbacher
- 1996
(Show Context)
Citation Context ...lly reasonable because insertions andsdeletions seldom occur in core regions. Thus, we also employ this assumption in thisspaper.sA variety of studies have been done for the protein threading problem =-=[3,5,8,s10,12,13,18]-=-. However, there are only a few studies that try to find an optimal thread-sing (i.e., a threading with the minimum score) [5, 12,13, 181. Bryant and Lawrence usedsexhaustive search to examine all pos... |

6 |
Proof verification and hardness of approximation algorithms
- Arora, Lund, et al.
- 1992
(Show Context)
Citation Context ...roximate solution. If there exists an approximation algorithm with performance ratio f(n) for a problem X where n denotes the size of an input, we say that X can be approximated within a factor f (n) =-=[1]-=-. 3 Hardness Results First, we show that PROTEIN THREADING is MAX SNPhard even if the maximum vertex degree is bounded by a constant B. From this result, a constant size lower bound of performance rat... |

1 |
Learning score function for protein threading using linear programming
- Tashimo, Akutsu
- 1996
(Show Context)
Citation Context ...point of predictive accuracy if they were applied to the threading problem. Thus, we are currently studying a method for deriving a good score function from known three-dimensional protein structures =-=[14]. Det-=-ails about the method and the experimental results will be reported elsewhere. Acknowledgment This work was partially supported by the Grant-in-Aid for Scientific Research on Priority Areas, "Gen... |