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21
Protein Folding in the HydrophobicHydrophilic (HP) Model is NPcomplete
, 1998
"... One of the simplest and most popular biophysical models of protein folding is the hydrophobichydrophilic (HP) model. The HP model abstracts the hydrophobic interaction in protein folding by labeling the amino acids as hydrophobic (H for nonpolar) or hydrophilic (P for polar). Chains of amino acid ..."
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Cited by 114 (0 self)
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One of the simplest and most popular biophysical models of protein folding is the hydrophobichydrophilic (HP) model. The HP model abstracts the hydrophobic interaction in protein folding by labeling the amino acids as hydrophobic (H for nonpolar) or hydrophilic (P for polar). Chains of amino acids are con6gured as selfavoiding nalks on the 3D cubic lattice, where an optimal conformation maximizes the number of adjacencies between H’s. In this paper, the protein folding problem under the HP model on the cubic lattice is shown to be NPcomplete. This means that the protein folding problem belongs to a large set of problems that are believed to be computationally intractable.
Algorithmic aspects of protein structure similarity
 In 40th Annual Symposium on Foundations of Computer Science
, 1999
"... We show that calculating contact map overlap (a measure of similarity of protein structures) is NPhard, but can be solved in polynomial time for several interesting and relevant special cases. We identify an important special case of this problem corresponding to selfavoiding walks, and prove a dec ..."
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Cited by 55 (3 self)
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We show that calculating contact map overlap (a measure of similarity of protein structures) is NPhard, but can be solved in polynomial time for several interesting and relevant special cases. We identify an important special case of this problem corresponding to selfavoiding walks, and prove a decomposition theorem and a corollary approximation result for this special case. These are the rst approximation algorithms with guaranteed error bounds, and NPcompleteness results in the literature in the area of protein structure alignment/fold recognition for measures of structure similarity of practical interest. A
Rapid protein sidechain packing via tree decomposition
 Research in Computational Molecular Biology, Lecture Notes in Computer Science
, 2005
"... Abstract. This paper proposes a novel tree decomposition based sidechain assignment algorithm, which can obtain the globally optimal solution of the sidechain packing problem very efficiently. Theoretically, the computational complexity of this algorithm is O((N +M)n tw+1 rot) where N is the numbe ..."
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Cited by 20 (1 self)
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Abstract. This paper proposes a novel tree decomposition based sidechain assignment algorithm, which can obtain the globally optimal solution of the sidechain packing problem very efficiently. Theoretically, the computational complexity of this algorithm is O((N +M)n tw+1 rot) where N is the number of residues in the protein, M the number of interacting residue pairs, nrot the average number of rotamers for each residue and tw( = O(N 2 3 log N)) the tree width of the residue interaction graph. Based on this algorithm, we have developed a sidechain prediction program SCATD (Side Chain Assignment via Tree Decomposition). Experimental results show that after the Goldstein DEE is conducted, nrot is around 3.5, tw is only 3 or 4 for most of the test proteins in the SCWRL benchmark and less than 10 for all the test proteins. SCATD runs up to 90 times faster than SCWRL 3.0 on some large proteins in the SCWRL benchmark and achieves an average of five times faster speed on all the test proteins. If only the postDEE stage is taken into consideration, then our treedecomposition based energy minimization algorithm is more than 200 times faster than that in SCWRL 3.0 on some large proteins. SCATD is freely available for academic research upon request. 1
Fold recognition by predicted alignment accuracy
 ACM/IEEE Transactions on Computational Biology and Bioinformatics
, 2005
"... Abstract—One of the key components in protein structure prediction by protein threading technique is to choose the best overall template for a given target sequence after all the optimal sequencetemplate alignments are generated. The chosen template should have the best alignment with the target se ..."
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Cited by 15 (6 self)
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Abstract—One of the key components in protein structure prediction by protein threading technique is to choose the best overall template for a given target sequence after all the optimal sequencetemplate alignments are generated. The chosen template should have the best alignment with the target sequence since the threedimensional structure of the target sequence is built on the sequencetemplate alignment. The traditional method for template selection is called Zscore, which uses a statistical test to rank all the sequencetemplate alignments and then chooses the firstranked template for the sequence. However, the calculation of Zscore is timeconsuming and not suitable for genomescale structure prediction. Zscores are also hard to interpret when the threading scoring function is the weighted sum of several energy items of different physical meanings. This paper presents a Support Vector Machine (SVM) regression approach to directly predict the alignment accuracy of a sequencetemplate alignment, which is used to rank all the templates for a specific target sequence. Experimental results on a largescale benchmark demonstrate that SVM regression performs much better than the compositioncorrected Zscore method. SVM regression also runs much faster than the Zscore method. Index Terms—Protein structure prediction, protein threading, protein fold recognition, SVM regression. 1
Protein Structure Prediction by Linear Programming
, 2003
"... If the primary sequence of a protein is given, what is its threedimensional structure? This is one of the most important and dicult problems in molecular biology and has tremendous implication to proteomics. Over the last three decades, this issue has been intensely researched. Protein threading re ..."
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Cited by 13 (0 self)
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If the primary sequence of a protein is given, what is its threedimensional structure? This is one of the most important and dicult problems in molecular biology and has tremendous implication to proteomics. Over the last three decades, this issue has been intensely researched. Protein threading represents one of the most promising techniques. So far, there are many protein structure prediction computer programs based on protein threading; however, almost none incorporates the pairwise contact (interaction) potential explicitly in its energy function, although scientists believe that pairwise interactions are important for fold recognition targets. The underlying reason for ignoring the pairwise potential is that the protein threading problem is NPhard (i.e., it is unlikely to have a polynomialtime algorithm), if the pairwise interactions are treated rigorously.
A treedecomposition approach to protein structure prediction
 In Proc. 4th International IEEE Computer Society Computational Systems Bioinformatics Conference (CSB 2005
, 2005
"... This paper proposes a tree decomposition of protein structures, which can be used to efficiently solve two key subproblems of protein structure prediction: protein threading for backbone prediction and protein sidechain prediction. To develop a unified treedecomposition based approach to these two ..."
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Cited by 9 (1 self)
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This paper proposes a tree decomposition of protein structures, which can be used to efficiently solve two key subproblems of protein structure prediction: protein threading for backbone prediction and protein sidechain prediction. To develop a unified treedecomposition based approach to these two subproblems, we model them as a geometric neighborhood graph labeling problem. Theoretically, we can have a lowdegree polynomial time algorithm to decompose a geometric neighborhood graph G = (V, E) into components with size O(V  2 3 log V ). The computational complexity of the treedecomposition based graph labeling algorithms is O(V  ∆ tw+1) where ∆ is the average number of possible labels for each vertex and tw( = O(V  2 3 log V )) the tree width of G. Empirically, tw is very small and the treedecomposition method can solve these two problems very efficiently. This paper also compares the computational efficiency of the treedecomposition approach with the linear programming approach to these two problems and identifies the condition under which the treedecomposition approach is more efficient than the linear programming approach. Experimental result indicates that the treedecomposition approach is more efficient most of the time. 1
Solving the Protein Threading Problem in Parallel
 In IPDPS ’03: Proceedings of the 17th International Symposium on Parallel and Distributed Processing
, 2003
"... We propose a network flow formulation for protein threading and show its equivalence with the shortest path problem on a graph with a very particular structure. The underying Mixed Integer Programming (MIP) model proves to be very appropriate for the protein threading problemhuge reallife instanc ..."
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Cited by 6 (3 self)
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We propose a network flow formulation for protein threading and show its equivalence with the shortest path problem on a graph with a very particular structure. The underying Mixed Integer Programming (MIP) model proves to be very appropriate for the protein threading problemhuge reallife instances have been solved in a reasonable time by using only a Mixed Integer Optimizer instead of a specialpurpose branch&bound algorithm. The properties of the MIP model allow decomposition of the main problem on a large number of subproblems (tasks). We show in this paper that a branch&bound alike algorithm can be efficiently applied to solving in parallel these tasks, which leads to a significant reduction in the total running time. Computational experiments with huge problem instances are presented.
Protein threading based on multiple protein structure alignment
 Genome Inform. Ser. Workshop Genome Inform
, 1999
"... Protein threading, a method employed in protein threedimensional (3D) structure prediction was only proposed in the early 1990’s although predicting protein 3D structure from its given amino acid sequence has been around since 1970’s. Here we describe a protein threading method/system that we have ..."
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Cited by 4 (0 self)
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Protein threading, a method employed in protein threedimensional (3D) structure prediction was only proposed in the early 1990’s although predicting protein 3D structure from its given amino acid sequence has been around since 1970’s. Here we describe a protein threading method/system that we have developed based on multiple protein structure alignment. In order to compute multiple structure alignments, we developed a similar structure search program on massive parallel computers and a program for constructing a multiple structure alignment from pairwise structure alignments, where the latter is based on the center star method for sequence alignment. A simple dynamicprogramming based algorithm which uses a profile matrix obtained from the result of multiple structure alignment was also developed to compute a threading (i.e., an alignment between a target sequence and a known structure). Using this system, we participated in the threading category (category AL) of CASP3 (Third Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction). The results are discussed.
Fast molecular shape matching using contact maps
, 2002
"... In this paper, we study the problem of computing the similarity of two protein structures by measuring their contactmap overlap. Contactmap overlap abstracts the problem of computing the similarity of two polygonal chains as a graphtheoretic problem. In R 3,we present the first polynomial time al ..."
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Cited by 3 (1 self)
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In this paper, we study the problem of computing the similarity of two protein structures by measuring their contactmap overlap. Contactmap overlap abstracts the problem of computing the similarity of two polygonal chains as a graphtheoretic problem. In R 3,we present the first polynomial time algorithm with any guarantee on the approximation ratio for the 3dimensional problem. More precisely, we give an algorithm for the contactmap overlap problem with an approximation ratio of σ, where σ = min{σ(P1),σ(P2)} ≤O(n 1/2) is a decomposition parameter depending on the input polygonal chains P1 and P2. InR 2, we improve the running time of the previous best known approximation algorithm from O(n 6) to O(n 3 log n) at the cost of decreasing the approximation ratio by half. We also give hardness results for the problem in three dimensions, suggesting that approximating it better than O(n ε), for some ε>0, is hard. Key words: shape matching, molecular structures, contact maps, graph theory. 1.
Recent Advances in Solving the Protein Threading Problem
"... apport d e r echerche ISSN 02496399 ISRN INRIA/RR6253FR+ENG ..."
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Cited by 3 (1 self)
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apport d e r echerche ISSN 02496399 ISRN INRIA/RR6253FR+ENG