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Plaxco, Kevin W.; Gross, Michael L.

doi:10.1038/90349

Cited by 82 publications

(43 citation statements)

References 10 publications

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“…3 Investigation into the low intrinsic dimensionality of a͒ molecular dynamics ͑MD͒ may provide an answer to the Levinthal paradox for protein folding. 4 Experimental investigations indicate that unfolded proteins do not exhibit purely random structure and may in fact retain structural properties present in the folded states. [4][5][6] Computational evidence further suggests that excluded volume effects significantly constrain the unfolded ensemble.…”

Section: Introductionmentioning

confidence: 99%

“…4 Experimental investigations indicate that unfolded proteins do not exhibit purely random structure and may in fact retain structural properties present in the folded states. [4][5][6] Computational evidence further suggests that excluded volume effects significantly constrain the unfolded ensemble. 7 Lange and Grubmuller 3 demonstrated that the effective variables from a 90% linear dimensionality reduction ͑i.e., retaining 10% of the number of original variables͒ for a 5 ns protein simulation explain most of the variance observed in a 200 ns long simulation.…”

Section: Introductionmentioning

confidence: 99%

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Algorithmic dimensionality reduction for molecular structure analysis

Brown

Martin

Pollock

et al. 2008

The Journal of Chemical Physics

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Dimensionality reduction approaches have been used to exploit the redundancy in a Cartesian coordinate representation of molecular motion by producing low-dimensional representations of molecular motion. This has been used to help visualize complex energy landscapes, to extend the time scales of simulation, and to improve the efficiency of optimization. Until recently, linear approaches for dimensionality reduction have been employed. Here, we investigate the efficacy of several automated algorithms for nonlinear dimensionality reduction for representation of trans, trans-1,2,4-trifluorocyclo-octane conformation-a molecule whose structure can be described on a 2-manifold in a Cartesian coordinate phase space. We describe an efficient approach for a deterministic enumeration of ring conformations. We demonstrate a drastic improvement in dimensionality reduction with the use of nonlinear methods. We discuss the use of dimensionality reduction algorithms for estimating intrinsic dimensionality and the relationship to the Whitney embedding theorem. Additionally, we investigate the influence of the choice of high-dimensional encoding on the reduction. We show for the case studied that, in terms of reconstruction error root mean square deviation, Cartesian coordinate representations and encodings based on interatom distances provide better performance than encodings based on a dihedral angle representation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Algorithmic dimensionality reduction for molecular structure analysis

Brown

Martin

Pollock

et al. 2008

The Journal of Chemical Physics

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“…T he unfolded and denatured states of proteins have recently received significant attention from experimentalists (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) and theoreticians alike (14)(15)(16)(17)(18)(19)(20)(21). Because the unfolded state represents one half of the protein-folding free energy diagram, the presence of any residual structure in the unfolded state carries significant implications for both thermodynamics and kinetics of protein folding.…”

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confidence: 99%

Unusual compactness of a polyproline type II structure

Žagrović

Lipfert

Sorin

et al. 2005

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

130

150

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Polyproline type II (PPII) helix has emerged recently as the dominant paradigm for describing the conformation of unfolded polypeptides. However, most experimental observables used to characterize unfolded proteins typically provide only short-range, sequence-local structural information that is both time-and ensemble-averaged, giving limited detail about the long-range structure of the chain. Here, we report a study of a long-range property: the radius of gyration of an alanine-based peptide, Ace-(diaminobutyric acid) 2-(Ala)7-(ornithine)2-NH2. This molecule has previously been studied as a model for the unfolded state of proteins under folding conditions and is believed to adopt a PPII fold based on short-range techniques such as NMR and CD. By using synchrotron radiation and small-angle x-ray scattering, we have determined the radius of gyration of this peptide to be 7.4 ؎ 0.5 Å, which is significantly less than the value expected from an ideal PPII helix in solution (13.1 Å). To further study this contradiction, we have used molecular dynamics simulations using six variants of the AMBER force field and the GROMOS 53A6 force field. However, in all cases, the simulated ensembles underestimate the PPII content while overestimating the experimental radius of gyration. The conformational model that we propose, based on our small angle x-ray scattering results and what is known about this molecule from before, is that of a very flexible, fluctuating structure that on the level of individual residues explores a wide basin around the ideal PPII geometry but is never, or only rarely, in the ideal extended PPII helical conformation. molecular dynamics ͉ small angle x-ray scattering ͉ unfolded state of proteins T he unfolded and denatured states of proteins have recently received significant attention from experimentalists (1-13) and theoreticians alike (14-21). Because the unfolded state represents one half of the protein-folding free energy diagram, the presence of any residual structure in the unfolded state carries significant implications for both thermodynamics and kinetics of protein folding. With regards to thermodynamics, permanent structure in the unfolded state significantly lowers the entropy of the unfolded state, thereby affecting the free energy change of folding. With regards to kinetics, the presence of preformed native-like contacts potentially speeds up the folding process. When it comes to structure, a consensus has recently begun to emerge about a significant presence of the polyproline type II (PPII) backbone geometry in the unfolded͞denatured state (12,18,(20)(21)(22)(23)(24)(25). The evidence for this view comes predominantly from spectroscopic studies on model peptides (12, 22-28, 61, 62) and computer simulations (18,20,21,(29)(30)(31)(32)62).The unfolded state of proteins, in addition to being intrinsically important in the context of protein folding, presents a fruitful ''laboratory'' for studying the question of the relative importance of local and global structural information in protein s...

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“…Recently, the molecular origins of RDCs in denatured proteins have attracted considerable attention (29,32). Shortle and coworkers (1,(26)(27)(28) argue that denatured proteins retain some native-like topology in the denatured state.…”

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confidence: 99%

Statistical coil model of the unfolded state: Resolving the reconciliation problem

Jha

Colubri

Freed

et al. 2005

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

300

415

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An unfolded state ensemble is generated by using a self-avoiding statistical coil model that is based on backbone conformational frequencies in a coil library, a subset of the Protein Data Bank. The model reproduces two apparently contradicting behaviors observed in the chemically denatured state for a variety of proteins, random coil scaling of the radius of gyration and the presence of significant amounts of local backbone structure (NMR residual dipolar couplings). The most stretched members of our unfolded ensemble dominate the residual dipolar coupling signal, whereas the uniformity of the sign of the couplings follows from the preponderance of polyproline II and ␤ conformers in the coil library. Agreement with the NMR data substantially improves when the backbone conformational preferences include correlations arising from the chemical and conformational identity of neighboring residues. Although the unfolded ensembles match the experimental observables, they do not display evidence of nativelike topology. By providing an accurate representation of the unfolded state, our statistical coil model can be used to improve thermodynamic and kinetic modeling of protein folding. denatured state ͉ protein folding ͉ residual dipolar coupling ͉ nearest neighbor ͉ radius of gyration D enatured proteins are the initial state for mechanistic and thermodynamic studies of folding. The recent resurgence of interest in the unfolded state is partly motivated by the development of NMR methods that are capable of providing site-resolved structural information (1-7). These measurements indicate that unfolded proteins have far richer structural diversity than earlier believed, possibly even encoding the native topology (1,(8)(9)(10)(11).These works seem at odds with the classic studies by Tanford et al. (12,13), who demonstrated by using hydrodynamic methods that the global dimensions of denatured proteins exhibit the size dependence expected for self-avoiding ''random coil'' polymers. More recent measurements of the radius of gyration, R g , using small-angle scattering methods exhibit the same random coil scaling behavior with length R g ϰ N 0.585 (8,14). These observations are consistent with denatured proteins being random coils in good solvent conditions (15). This finding leads to the so-called ''reconciliation problem'' between the random coil scaling behavior and the presence of significant amounts of local structure in unfolded state (14, 16).However, Rose and Fitzkee (17) demonstrate that even a ''deliberately extreme'' model of chains composed of native-like segments connected by flexible residues also can reproduce random coil scaling behavior. Hence, the recapitulation of the scaling behavior provides only a weak test for any unfolded state model. Nevertheless, spectroscopic measurements, such as circular dichroism, indicate that most unfolded states, particularly chemicaldenatured proteins (8,13,18), have little secondary structure. Accordingly, the unrealistic native-like segment model is ruled out. More exacting...

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Cited by 82 publications

References 10 publications

Algorithmic dimensionality reduction for molecular structure analysis

Algorithmic dimensionality reduction for molecular structure analysis

Unusual compactness of a polyproline type II structure

Statistical coil model of the unfolded state: Resolving the reconciliation problem

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