Computational Complexity, Protein Structure Prediction, and the Levinthal Paradox

Ngo, Jacqueline; Marks, Joe; Karplus, Martin

doi:10.1007/978-1-4684-6831-1_14

Cited by 49 publications

(44 citation statements)

References 91 publications

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“…Further, our analysis provides a mathematical methodology for transferring performance guarantees on lattices to off-lattice models. These results partially answer the open question of Karplus et al (1994) concerning the complexity of protein folding models that include side chains. …”

supporting

confidence: 58%

Lattice and Off-Lattice Side Chain Models of Protein Folding: Linear Time Structure Prediction Better than 86% of Optimal

Hart¹,

Istrail²

1997

Journal of Computational Biology

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This paper considers the protein structure prediction problem for lattice and off-lattice 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 off-lattice 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 off-lattice model, the H P Tangent Spheres Side Chain model (HP-TSSC), that generalizes this model further by representing the backbone and side chains of proteins with tangent spheres. We describe algorithms for both of these models with mathematically guaranteed error bounds. In particular, we describe a linear time performance guaranteed approximation algorithm for the HP side chain model that constructs conformations whose energy is better than 86% of optimal in a face centered cubic lattice, and we demonstrate how this provides a 70% performance guarantee for the HP-TSSC model. This is the first algorithm in the literature for off-lattice protein structure prediction that has a rigorous performance guarantee. Our analysis of the HP-TSSC model builds off of the work of Dan& and Hannenhalli who have developed a 16/30 approximation algorithm for the HP model on the hexagonal close packed lattice. Further, our analysis provides a mathematical methodology for transferring performance guarantees on lattices to off-lattice models. These results partially answer the open question of Karplus et al. (1994) concerning the complexity of protein folding models that include side chains.

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supporting

confidence: 58%

Lattice and Off-Lattice Side Chain Models of Protein Folding: Linear Time Structure Prediction Better than 86% of Optimal

Hart¹,

Istrail²

1997

Journal of Computational Biology

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“…Many possible suggestions have been made to circumvent this problem, but the issue is still a subject of intense discussion. [48][49][50] These many degrees of freedom for peptides, however, do not couple at the low energies of about 200 cm À1 involved here. Thresholds for intramolecular vibrational redistribution (IVR) in kinetics are typically at least 1200 cm À1 [51] or 2200 cm À1 [52] and at low energies are even higher, [53,54] although the picture for very large molecules with soft modes may be different.…”

mentioning

confidence: 90%

Distal Charge Transport in Peptides

Schlag¹,

Sheu²,

Yang³

et al. 2007

Angew Chem Int Ed

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Biological systems often transport charges and reactive processes over substantial distances. Traditional models of chemical kinetics generally do not describe such extreme distal processes. In this Review, an atomistic model for a distal transport of information, which was specifically developed for peptides, is considered. Chemical reactivity is taken as the result of distal effects based on two-step bifunctional kinetics involving unique, very rapid motional properties of peptides in the subpicosecond regime. The bifunctional model suggests highly efficient transport of charge and reactivity in an isolated peptide over a substantial distance; conversely, a very low efficiency in a water environment was found. The model suggests ultrafast transport of charge and reactivity over substantial molecular distances in a peptide environment. Many such domains can be active in a protein.

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“…The number of possible conformations is exponential in the length of the protein sequence, and even powerful computational hardware is not capable of enumerating this space for even moderately large proteins. This observation led Levinthal [15] to raise a question about the paradoxical discrepancy between the enormous number of possible conformations and the fact that a large fraction of proteins of all sizes fold within minutes. While these observations appear contradictory they simply point to the lack of knowledge of a possible algorithmic structure that could guide an efficient search algorithm (see [15] for further discussion of this issue).…”

Section: Energy Minimizationmentioning

confidence: 99%

“…This observation led Levinthal [15] to raise a question about the paradoxical discrepancy between the enormous number of possible conformations and the fact that a large fraction of proteins of all sizes fold within minutes. While these observations appear contradictory they simply point to the lack of knowledge of a possible algorithmic structure that could guide an efficient search algorithm (see [15] for further discussion of this issue). Consequently, computational analyses of the protein folding process can provide insight into the inherent algorithmic difficulty of folding proteins.…”

Section: Energy Minimizationmentioning

confidence: 99%

“…Although a variety of methods have been proposed to perform structure prediction, this problem has been difficult to solve in a robust manner. For example, Ngo et al [15] note that "It is still not known whether there exists an efficient algorithm for predicting the structure of a protein from its amino acid sequence alone. Decades of research have failed to produce such an algorithm-yet Nature seems to solve the problem.…”

Section: Introductionmentioning

confidence: 99%

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On the Intractability of Protein Folding with a Finite Alphabet of Amino Acids

Atkins

Hart

1999

Algorithmica

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We describe a proof of NP-hardness for a lattice protein folding model whose instances contain protein sequences defined with a fixed, finite alphabet that contains 12 amino acid types. This lattice model represents a protein's conformation as a self-avoiding path that is embedded on the three-dimensional cubic lattice. A contact potential is used to determine the energy of a sequence in a given conformation; a pair of amino acids contributes to the conformational energy only if they are adjacent on the lattice. This result overcomes a significant weakness of previous intractability results, which do not examine protein folding models that have a finite alphabet of amino acids together with physically interesting conformations.

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Computational Complexity, Protein Structure Prediction, and the Levinthal Paradox

Cited by 49 publications

References 91 publications

Lattice and Off-Lattice Side Chain Models of Protein Folding: Linear Time Structure Prediction Better than 86% of Optimal

Lattice and Off-Lattice Side Chain Models of Protein Folding: Linear Time Structure Prediction Better than 86% of Optimal

Distal Charge Transport in Peptides

On the Intractability of Protein Folding with a Finite Alphabet of Amino Acids

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