Exactness of the annealed and the replica symmetric approximations for random heteropolymers

Bastolla, Ugo; Grassberger, Peter

doi:10.1103/physreve.63.031901

Cited by 12 publications

(12 citation statements)

References 34 publications

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“…Random sequences have a bimodal overlap distribution, in qualitative agreement with the mean-field theory by Shakhnovich and Gutin, with a peak at small overlap that shrinks and shifts towards smaller but non-vanishing [16] values as system size increases, and a peak at large q terminating with a delta in q = 1. It seems that this peak shrinks towards q = 1 as system size increases, although it is not clear whether it vanishes in the thermodynamic limit, as predicted by mean-field theory.…”

Section: Discussionsupporting

confidence: 72%

“…With respect to the peak at low q, we mention here that a detailed study examining very long chains [16] shows that the typical overlap for an unrelated sequence is not at q = 0 but at a small value q 0 (c), which decreases as the fraction of contacts c increases. This non-vanishing average overlap is due to contacts which are local along the chain.…”

Section: Random Interactionsmentioning

confidence: 96%

“…In a previous work we found, however, that the typical overlap q 0 does not vanish in the thermodynamic limit [16].…”

Section: Random Sequencesmentioning

confidence: 99%

“…a e-mail: bastolla@mpikg-golm.mpg.de b e-mail: ugo@chemie.fu-berlin. de We showed in [16], examining chains of very large size, that the overlap between unrelated structures is very small but does not vanish in the thermodynamic limit. This is due to the presence of short-range contacts and is even more true for protein-like structures, because of the presence of secondary structure.…”

Section: Introductionmentioning

confidence: 97%

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Overlap distribution in random and designed heteropolymers

Bastolla

2001

The European Physical Journal E

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We study the overlap between low-energy states in lattice models of heteropolymers with contact interactions. The overlap distribution gives information on the degree of correlation in the energy landscape. Designed sequences have rather correlated energy landscapes, which favor fast folding kinetics. Chains with random interactions have much less correlated energy landscapes. It is indeed believed that the meanfield theory for this model coincides with the Random Energy Model, whose different low-energy states are completely unrelated. This picture has been supported by numerical studies of maximally compact configurations. Without applying this constraint, we find that the overlap distribution is indeed bimodal as expected, but it has a broad peak at large overlap, indicating a non-vanishing width for the valleys of low-energy states. This feature probably plays an important role in the kinetics of the model. It is not evident that the range of such correlations shrinks to zero for large systems. The range of the correlations seems to be influenced by the number of contacts per residue in the ground state: the smaller this quantity, the larger the correlations.

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Section: Discussionsupporting

confidence: 72%

Section: Random Interactionsmentioning

confidence: 96%

“…In a previous work we found, however, that the typical overlap q 0 does not vanish in the thermodynamic limit [16].…”

Section: Random Sequencesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Overlap distribution in random and designed heteropolymers

Bastolla

2001

The European Physical Journal E

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“…Finally, several numerical studies 36,37 have focused on the ⌰ point of random bonds models and have argued that its location is extremely well approximated by an annealed computation. Once again, this confirms that Eq.…”

Section: Liquid Solution and The ⌰-Pointmentioning

confidence: 99%

Glassy phases in random heteropolymers with correlated sequences

Müller

Mézard

Montanari

2004

The Journal of Chemical Physics

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We develop an analytic approach for the study of lattice heteropolymers and apply it to copolymers with correlated Markovian sequences. According to our analysis, heteropolymers present three different dense phases depending upon the temperature, the nature of the monomer interactions, and the sequence correlations: (i) a liquid phase, (ii) a "soft glass" phase, and (iii) a "frozen glass" phase. The presence of the intermediate "soft glass" phase is predicted, for instance, in the case of polyampholytes with sequences that favor the alternation of monomers. Our approach is based on the cavity method, a refined Bethe-Peierls approximation adapted to frustrated systems. It amounts to a mean-field treatment in which the nearest-neighbor correlations, which are crucial in the dense phases of heteropolymers, are handled exactly. This approach is powerful and versatile; it can be improved systematically and generalized to other polymeric systems.

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How to guarantee optimal stability for most representative structures in the protein data bank

et al. 2001

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We proposed recently an optimization method to derive energy parameters for simplified models of protein folding. The method is based on the maximization of the thermodynamic average of the overlap between protein native structures and a Boltzmann ensemble of alternative structures. Such a condition enforces protein models whose ground states are most similar to the corresponding native states. We present here an extensive testing of the method for a simple residue-residue contact energy function and for alternative structures generated by threading. The optimized energy function guarantees high stability and a well-correlated energy landscape to most representative structures in the PDB database. Failures in the recognition of the native structure can be attributed to the neglect of interactions between different chains in oligomeric proteins or with cofactors. When these are taken into account, only very few X-ray structures are not recognized. Most of them are short inhibitors or fragments and one is a structure that presents serious inconsistencies. Finally, we discuss the reasons that make NMR structures more difficult to recognizeCopyright 2001 Wiley-Liss, Inc.

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Exactness of the annealed and the replica symmetric approximations for random heteropolymers

Cited by 12 publications

References 34 publications

Overlap distribution in random and designed heteropolymers

Overlap distribution in random and designed heteropolymers

Glassy phases in random heteropolymers with correlated sequences

How to guarantee optimal stability for most representative structures in the protein data bank

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