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73
Fast protein folding in the hydrophobichydrophilic model within threeeights of optimal
 1ZDD 34 1045 4.0 2.703 3.12 1Q2N 0.66 0.61 1VII 36 14280 7.4 3.047 12.59 1UNC 0.74 0.70 1EOM 37 36000 3.4 3.093 17.41 1I5H 0.47 0.49 1EDO 46 36000 7.2 3.656 11.54 1NBL 0.55 0.56 2IGD 61 174960 11.5 7.469 8.01 1MVK 0.79 0.74 1YPA 64 420840 9.4 6.687 0.34 2
, 1996
"... We present performanceguaranteed approximation algorithms for the protein folding problem in the hydrophobichydrophilic model (Dill, 1985). Our algorithms are the first approximation algorithms in the literature with guaranteed performance for this model (Dill, 1994). The hydrophobichydrophilic m ..."
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Cited by 68 (4 self)
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We present performanceguaranteed approximation algorithms for the protein folding problem in the hydrophobichydrophilic model (Dill, 1985). Our algorithms are the first approximation algorithms in the literature with guaranteed performance for this model (Dill, 1994). The hydrophobichydrophilic model abstracts the dominant force of protein folding: the hydrophobic interaction. The protein is modeled as a chain of amino acids of length n that are of two types; H (hydrophobic, i.e., nonpolar) and P (hydrophilic, i.e., polar). Although this model is a simplification of more complex protein folding models, the protein folding structure prediction problem is notoriously difficult for this model. Our algorithms have conformation that has linear (3n) or quadratic time and achieve a threedimensional protein a guaranteed free energy no worse than threeeighths of optimal. This result answers the open problem of Ngo et al. (1994) about the possible existence of an efficient approximation algorithm with guaranteed performance for protein structure prediction in any wellstudied model of protein folding. By achieving speed and nearoptimality simultaneously, our algorithms rigorously capture salient features of the recently proposed framework of protein folding by Sali et al. (1994). Equally important, the final conformations of our algorithms have significant secondary structure (antiparallel sheets, ^sheets, compact hydrophobic core). Furthermore, hypothetical folding pathways can be described for our algorithms that fit within the framework of diffusioncollision protein folding proposed by Karplus and Weaver (1979). Computational limitations of algorithms that compute the optimal conformation have restricted their applicability to short sequences (length < 90). Because our algorithms trade computational accuracy for speed, they can construct nearoptimal conformations in linear time for sequences of any size. 1.
Folding and Unfolding in Computational Geometry
"... Three open problems on folding/unfolding are discussed: (1) Can every convex polyhedron be cut along edges and unfolded at to a single nonoverlapping piece? (2) Given gluing instructions for a polygon, construct the unique 3D convex polyhedron to which itfolds. (3) Can every planar polygonal chain ..."
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Cited by 54 (4 self)
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Three open problems on folding/unfolding are discussed: (1) Can every convex polyhedron be cut along edges and unfolded at to a single nonoverlapping piece? (2) Given gluing instructions for a polygon, construct the unique 3D convex polyhedron to which itfolds. (3) Can every planar polygonal chain be straightened?
Recognizing Native Folds by the Arrangement of Hydrophobic and Polar Residues
, 1995
"... ured in standard deviation units) than has been previously demonstrated by more sophisticated methods. The arrangement of hydrophobic and polar residues alone as evaluated by our novel scoring scheme, is unexpectedly effective at recognizing native folds in general. It is surprising that a simple bi ..."
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Cited by 31 (6 self)
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ured in standard deviation units) than has been previously demonstrated by more sophisticated methods. The arrangement of hydrophobic and polar residues alone as evaluated by our novel scoring scheme, is unexpectedly effective at recognizing native folds in general. It is surprising that a simple binary pattern of hydrophobic and polar residues apparently selects a given unique fold topology. 7 1995 Academic Press Limited *Corresponding author Keywords: protein folding; hydrophobic interaction; fold recognition; contact potential; threading Introduction Since the classic work by Kauzmann (1959), it has been hypothesized that hydrophobic interactions play a major role in organizing and stabilizing the architecture of proteins. This phenomenon, loosely defined, is related to the relative insolubility of nonpolar substances in water (Tanford, 1980). It has long been observed that residues with hydrophobic sidechains tend to segregate into the interior of a globular protein, thus con
Lattice and OffLattice Side Chain Models of Protein Folding: Linear Time Structure Prediction Better Than 86% of Optimal (Extended Abstract)
 J. Comput. Biol
, 1997
"... ) William E. Hart Sorin Istrail y Abstract This paper considers the protein structure prediction problem for lattice and offlattice protein folding models that explicitly represent side chains. Lattice models of proteins have proven extremely useful tools for reasoning about protein folding i ..."
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Cited by 26 (2 self)
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) William E. Hart Sorin Istrail y Abstract This paper considers the protein structure prediction problem for lattice and offlattice protein folding models that explicitly represent side chains. Lattice models of proteins have proven extremely useful tools for reasoning about protein folding in unrestricted continuous space through analogy. This paper provides the first illustration of how rigorous algorithmic analyses of lattice models can lead to rigorous algorithmic analyses of offlattice models. We consider two side chain models: a lattice model that generalizes the HP model (Dill 85) to explicitly represent side chains on the cubic lattice, and a new offlattice model, the HP Tangent Spheres Side Chain model (HPTSSC), that generalizes this model further by representing the backbone and side chains of proteins with tangent spheres. We describe algorithms with mathematically guaranteed error bounds for both of these models. In particular, we describe a linear time performanc...
EQUIENERGY SAMPLER WITH APPLICATIONS IN STATISTICAL INFERENCE AND STATISTICAL MECHANICS
, 2006
"... We introduce a new sampling algorithm, the equienergy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperaturedomain methods, the equienergy sampler, utilizing the temperature–energy duality, targets the energy directly. The focus on the energy func ..."
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Cited by 26 (4 self)
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We introduce a new sampling algorithm, the equienergy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperaturedomain methods, the equienergy sampler, utilizing the temperature–energy duality, targets the energy directly. The focus on the energy function not only facilitates efficient sampling, but also provides a powerful means for statistical estimation, for example, the calculation of the density of states and microcanonical averages in statistical mechanics. The equienergy sampler is applied to a variety of problems, including exponential regression in statistics, motif sampling in computational biology and protein folding in biophysics.
An immune algorithm for protein structure prediction on lattice models
 IEEE Transactions on Evolutionary Computation
"... by the clonal selection principle, which has been designed for the protein structure prediction problem (PSP). The proposed IA employs two special mutation operators, hypermutation and hypermacromutation, to allow for effective searching, and an aging mechanism, a new immune inspired operator, devis ..."
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Cited by 22 (6 self)
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by the clonal selection principle, which has been designed for the protein structure prediction problem (PSP). The proposed IA employs two special mutation operators, hypermutation and hypermacromutation, to allow for effective searching, and an aging mechanism, a new immune inspired operator, devised to enforce diversity in the population during evolution. When cast as an optimization problem, the PSP can be seen as discovering a protein conformation with minimal energy. The proposed IA was tested on well known PSP lattice models, the HP model in 2D and 3D square lattices’, and the functional model protein, which is a more realistic biological model. Our experimental results demonstrate that the proposed Immune Algorithm is very competitive with existing stateofart algorithms for the PSP on lattice models. Index Terms — Immune algorithms, clonal selection algorithms, hypermutation operator, hypermacromutation operator, aging operator, protein structure prediction problem, 2D HP model, 3D HP model, functional model proteins. I.
The Protein Structure Prediction Problem: A Constraint Optimization Approach using a New Lower Bound
, 2000
"... The protein structure prediction problem is one of the most (if not the most) important problem in computational biology. This problem consists of nding the conformation of a protein with minimal energy. Because of the complexity of this problem, simplied models like Dill's HPlattice model [15, ..."
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Cited by 21 (2 self)
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The protein structure prediction problem is one of the most (if not the most) important problem in computational biology. This problem consists of nding the conformation of a protein with minimal energy. Because of the complexity of this problem, simplied models like Dill's HPlattice model [15, 16] have become a major tool for investigating general properties of protein folding. Even for this simplied model, the structure prediction problem has been shown to be NPcomplete [5, 7]. We describe a constraint formulation of the HPmodel structure prediction problem, and present the basic constraints and search strategy. Of course, the simple formulation would not lead to an ecient algorithm. We therefore describe redundant constraints to prune the search tree. Furthermore, we need bounding function for the energy of an HPprotein. We introduce a new lower bound based on partial knowledge about the nal conformation (namely the distribution of Hmonomers to layers). 1 Intr...
How are Model Protein Structures Distributed in Sequence Space?
, 1997
"... We analyze the sequence to structure map for all uniquely folding sequences of short HP (hydrophobicpolar) model proteins on a square lattice (Lau and Dill 1989; Dill et al. 1995) to investigate aspects we consider relevant for evolution. Ranking structures by their frequencies we find few very fr ..."
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Cited by 21 (1 self)
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We analyze the sequence to structure map for all uniquely folding sequences of short HP (hydrophobicpolar) model proteins on a square lattice (Lau and Dill 1989; Dill et al. 1995) to investigate aspects we consider relevant for evolution. Ranking structures by their frequencies we find few very frequent and many rare structures. The distribution can be empirically described by a generalized Zipf's law. All structures are relatively compact, yet the most compact ones are rare. Most sequences falling to the same structure belong to "neutral nets". These graphs in sequence space are connected by point mutations and centered around prototype sequences which tolerate the largest number (up to 55%) of neutral mutations. Profiles have been derived from these homologous sequences. Frequent structures conserve hydrophobic cores only while rare ones are sensitive to surface mutations as well. Shape space covering, i.e. the ability to transform any structure into most others with few point muta...
A Complete and Effective Move Set for Simplified Protein Folding
 7th Annual International Conference on Research in Computational Molecular Biology (RECOMB) 2003
, 2003
"... We present new lowest energy configurations for several large benchmark problems for the twodimensional hydrophobichydrophilic model. We found these solutions with a generic implementation of tabu search using an apparently novel set of transformations that we call pull moves. ..."
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Cited by 21 (1 self)
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We present new lowest energy configurations for several large benchmark problems for the twodimensional hydrophobichydrophilic model. We found these solutions with a generic implementation of tabu search using an apparently novel set of transformations that we call pull moves.
CHAIN GROWTH ALGORITHMS FOR HPTYPE LATTICE PROTEINS
, 1997
"... We describe a novel fast straightforward folding algorithm for HP (hydrophobic polar) t,ype lattice proteins. It, is designed after the concept of unguided, cotranslational folding of a nascent. peptide. It is tlcterminist~ic and runs in O ( 17) in the chain length. Acruracy of prediction is gove ..."
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Cited by 17 (1 self)
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We describe a novel fast straightforward folding algorithm for HP (hydrophobic polar) t,ype lattice proteins. It, is designed after the concept of unguided, cotranslational folding of a nascent. peptide. It is tlcterminist~ic and runs in O ( 17) in the chain length. Acruracy of prediction is governed by t,hr searc11 tlcl)th of t,llc, algorithtn that is “looked ahead ” at each chain growth st el’. I,ong range interactions are significantly incrcas<~tl and c’rlergy barriers become less prohibitive with increasing search depth. ‘I’tle csfficiency of sequential folding is test & arid rc:sults comparetl to related methods. All characterist its of the HPmotlcl buch as formation of a hydrophobic core and overall compact structures are observed. Sinccl the procrt1ln.c is very fast and flexible we obtain a useful tool to approxirnatt ~ t.he sqricnce t.0 st,ructlire mapping of t)iopotymers in general antI to study the complex interplay of folding strat,rgies, pot,entials and alphabets with large ensembles of random structures.