Optimal neural networks for protein-structure prediction

Head‐Gordon, Teresa; Stillinger, Frank H.

doi:10.1103/physreve.48.1502

Cited by 22 publications

(36 citation statements)

References 28 publications

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“…For sequences with a typical fraction of hydrophobic residues, we find that the nonrandomness can be interpreted as anticorrelations. This interpretation emerges from a simple Ising model of antiferromagnetic interactions among the residues.Given the impact our results might have on the issue of how permissive with respect to sequence specificity the protein folding process is, we have carried out the same analysis for a toy model (7,8), for which unbiased samples of folding and nonfolding sequences can be obtained. This model, hereafter denoted the AB model, consists of chains of two kinds of "amino acids" interacting with Lennard-Jones potentials.…”

mentioning

confidence: 99%

Evidence for nonrandom hydrophobicity structures in protein chains.

Irbäck

Peterson

Potthast

1996

Proc. Natl. Acad. Sci. U.S.A.

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The question of whether proteins originate from random sequences of amino acids is addressed. A statistical analysis is performed in terms of blocked and random walk values formed by binary hydrophobic assignments of the amino acids along the protein chains. Also, recent work on simplified models suggest nonrandomness (4,5). In these studies a large number of randomly selected sequences were investigated, and it was found that only a small fraction of them folded easily into a thermodynamically stable state.In this work we study the statistical distribution of hydrophobicity by using methods different from the run test in ref. 1. Along the same lines as in ret 3, rather than analyzing raw sequences of hydrophobicity, we focus on the corresponding random walk representation. In this way, the analysis is more sensitive to long-range correlations along the sequence. Our analysis has been carried out using two different methods, which differ substantially from what is used in ref. 3, although the starting point is similar. First, we form block variables, and study how the behavior of these depends on the block size. When applied to the SWISS-PROT data base (6) of functional proteins, this method yields clear evidence for nonrandomness. In addition, we have performed a Fourier analysis based on the random walk representation. In this analysis we find nonrandom behavior at the wavelength corresponding to a-helix structure, as one might have expected, but also at large wavelengths.In our analysis, we have divided the sequences into groups corresponding to different fractions of hydrophobic residues. This division is important, because the results for different groups deviate in different directions from those for random sequences. For sequences with a typical fraction of hydrophobic residues, we find that the nonrandomness can be interpreted as anticorrelations. This interpretation emerges from a simple Ising model of antiferromagnetic interactions among the residues.Given the impact our results might have on the issue of how permissive with respect to sequence specificity the protein folding process is, we have carried out the same analysis for a toy model (7,8), for which unbiased samples of folding and nonfolding sequences can be obtained. This model, hereafter denoted the AB model, consists of chains of two kinds of "amino acids" interacting with Lennard-Jones potentials. We have examined the behavior of 300 randomly selected chains of length 20 in this model (9). Of these, only 10% were found to have reasonable folding properties. Analyzing these sequences with the same methods as being used for the functional proteins, we obtain results that are qualitatively very similar to those for proteins with a typical fraction of hydrophobic residues. In particular, we again find deviations from random behavior that correspond to anticorrelations. One should keep in mind that the toy model chains are quite short and highly simplified as compared with functional proteins. Nevertheless, it is appealing to attempt an ...

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mentioning

confidence: 99%

Evidence for nonrandom hydrophobicity structures in protein chains.

Irbäck

Peterson

Potthast

1996

Proc. Natl. Acad. Sci. U.S.A.

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“…However, despite the availability of published global minimum structures 42,43 for all n-mers of the two-dimensional AB model for n ϭ 3 . .…”

Section: Choice Of the Ab Model Data Setsmentioning

confidence: 91%

“…The models used here to provide further substrates for the simulated chaperone system are the two-and three-dimensional forms of the off-lattice model first introduced by Stillinger and Head-Gordon [42][43][44] and later extended into three dimensions by Irbäck and Potthast. [45][46][47] These are two-state (HP) models with no explicit representation of side chains or hydrogen bonding, so able to provide only a coarse-grained approximation to the complexities of real proteins.…”

Section: The "Ab" Off-lattice Protein Modelsmentioning

confidence: 99%

Application of a chaperone‐based refolding method to two‐ and three‐dimensional off‐lattice protein models

Gorse

2002

Biopolymers

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A model of protein-chaperone interaction as a two-phase (unfolding/refolding) iterative annealing mechanism able to promote structural segregation of hydrophobic and hydrophilic monomers and thereby facilitate access to nativelike states has recently been applied successfully to two 22-mers of the Honeycutt and Thirumalai BLN (hydrophobic, hydrophilic, neutral) heteropolymer model. This technique is here applied to a much wider data set: 94 8-mers of the off-lattice protein model originally presented in two dimensions by Stillinger and Head-Gordon, and later extended into three dimensions by Irbäck and Potthast; the model chaperone is shown to be equally successful, and by progressive elaboration of the chaperone model as in the earlier BLN model work, to be utilizing very similar underlying mechanisms. It is demonstrated that on average, contacts with the model chaperone give rise to a consistent movement in structure space in the direction of more nativelike structures; this method of global minimization does not therefore rely fundamentally on random search. Insofar as the responses to the chaperone of the two- and three-dimensional forms of the substrate model do differ, this can be interpreted as reflecting the different handling of hydrophilic monomers in the models-in particular, whether there is active repulsion between these and monomers of hydrophobic character. The chaperone-induced refolding method is also tested on a set of 220 9-mer chains of each version of the substrate model, where it is seen that the two-dimensional model, with its more clearly distinguished roles for the hydrophobic and hydrophilic monomers, shows a more favorable scaling behavior.

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“…Another direction is exploring ways to incorporate additional partial information that scientists have about the structure of proteins. For example, scientists appear able to predict the secondary structure of portions of proteins with high but not perfect accurary 11,5 ], and it would seem useful to be able to utilize these predictions in the global optimization algorithm in some manner.…”

Section: Conclusion and Future Resultsmentioning

confidence: 99%

Global optimization methods for protein folding problems

Byrd¹,

Eskow²,

Hoek³

et al. 1995

Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein F

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Abstract. The problem of nding the naturally occurring structure of a protein is believed to correspond to minimizing the free, or potential, energy of the protein. This is generally a very di cult global optimizationproblem, with a large number of parameters and a huge number of local minimizers including many with function values near that of the global minimizer. This paper presents a new global optimization method for such problems. The method consists of an initial phase that locates some reasonablylow local minimizers o f the energy function, followed by the main phase that progresses from the best current local minimizers to even lower local minimizers. The method combines portions that work on small subsets of the parameters, including small-scale global optimizations using stochastic methods, with local minimizations involving all the parameters. In computational tests on the protein polyalanine with up to 58 amino acids (116 internal parameters), the method appears to be very successful in nding the lowest energy structures. The largest case is particularly signi cant because the lowest energy structures that are found include ones that exhibit interesting tertiary as opposed to just secondary structure.

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Optimal neural networks for protein-structure prediction

Cited by 22 publications

References 28 publications

Evidence for nonrandom hydrophobicity structures in protein chains.

Evidence for nonrandom hydrophobicity structures in protein chains.

Application of a chaperone‐based refolding method to two‐ and three‐dimensional off‐lattice protein models

Global optimization methods for protein folding problems

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