Protein states and proteinquakes.

Ansari, Anjum; Berendzen, Joel; Bowne, Samuel F.; Frauenfelder, Hans; Iben, Icko; Sauke, Todd B.; Erramilli, Shyamsunder; Young, Robert D.

doi:10.1073/pnas.82.15.5000

Cited by 808 publications

(634 citation statements)

References 35 publications

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“…Experimental measurements of the rebinding kinetics of CO to myoglobin indeed observed a stretched-exponential time dependence [5][6][7][8]. These observations led Frauenfelder et al [5[ to propose the existence of a hierarchy of motions occurring at various timescales, which results from an ensemble of nearly degenerate states separated by a hierarchical distribution of enthalpic energy barriers.…”

Section: Discussionmentioning

confidence: 99%

“…Proteins exhibit motions on a very wide range of timescales from picoseconds (ps) [1][2][3] to seconds [4] (as studied by hydrogen exchange experiments). Experimental studies on myoglobin suggest the existence of a hierarchy of motions occurring at various timescales and resulting from an ensemble of nearly degenerate states separated by a distribution of enthalpic energy barriers [5][6][7][8]. On longer timescales (milliseconds to seconds) many proteins seem to follow an energy-like funnel to the folded state [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…In support of these observations Garcfa [29] showed that the fluctuations of a protein in solution are best described in terms of large-amplitude nonlinear motions. Molecular dynamics (MD) simulations, ligand recombination [30], pressure relaxation [7,8], time resolved X-ray crystallography [31 ] and vibrational echo studies [1][2][3] give information about the lower end of the funnel or energy landscape that is sampled in the folded state. Computational evidence (MD and Monte Carlo (MC) simulations) for the existence of these substates have been previously discussed in the literature [29,[32][33][34].…”

Section: Introductionmentioning

confidence: 99%

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Multi-basin dynamics of a protein in a crystal environment

Garcı́a

Blumenfeld

Hummer

et al. 1997

Physica D: Nonlinear Phenomena

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The dynamics of the small protein crambin is studied in the crystal environment by means of a 5.1 nanoseconds molecular dynamics (MD) simulation. The resulting trajectory is analyzed in terms of a small set of nonlinear dynamical modes that best describe the molecule's fluctuations. These modes are nonlinear in the sense that they describe a trajectory exhibiting multiple transitions among local minima at various timescales. Nonlinear modes are responsible for most of the protein atomic fluctuations. An ultrametric hierarchy of sampled local minima describes the protein trajectory when structures are classified in terms of their interconfigurational mean squared distance. Transitions among minima involve small changes in the relative atomic positions of many atoms in the protein. The character of the MD trajectory fits within the framework of rugged energy landscape dynamics. This MD simulation clarifies the unique statistical features of the barriers between minima in the energy-like configurational landscape. Longer timescale dynamics seem to sample transitions between minima separated by relatively higher barriers. The MD trajectory of the system in configurational space can be described in terms of diffusion of a particle in real space with a waiting time distribution due to partial trapping in shallow minima. A description of the dynamics in terms of an open Newtonian system (the protein) coupled to a stochastic system (the solvent and fast quasiharmonic modes of the protein) reveals that the system loses memory of its configurational space within a few picoseconds. The diffusion of the protein in configurational space is anomalous in the sense that the mean square displacement increases sublinearly with time, i.e., as a power law with an exponent that is smaller than unity.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi-basin dynamics of a protein in a crystal environment

Garcı́a

Blumenfeld

Hummer

et al. 1997

Physica D: Nonlinear Phenomena

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“…For example, 0006-2960/88/0427-2132$01.50/0 a side chain may have rotated, some hydrogen bonds may have shifted, a single helix may be displaced, or small movements may occur involving entire structural domains (Austin et al, 1975;Frauenfelder et al, 1979;Hartmann et al, 1982;Ringe et al, 1985). Recently, a hierarchical model for such substates has been proposed, each level of the hierarchy being characterized by a specific interconversion time scale and energy (Ansari et al, 1985(Ansari et al, , 1987Frauenfelder & Gratton, 1985;Kuriyan et al, 1987).…”

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confidence: 99%

Effect of unfolding on the tryptophanyl fluorescence lifetime distribution in apomyoglobin

Bismuto¹,

Gratton²,

Irace³

1988

Biochemistry

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Proteins exhibit, even in their native state, a large number of conformations differing in small details (substates). The fluorescence lifetime of tryptophanyl residues can reflect the microenvironmental characteristics of these subconformations. We have analyzed the lifetime distribution of the unique indole residue of tuna apomyoglobin (Trp A-12) during the unfolding induced by temperature or guanidine hydrochloride. The results show that the increase of the temperature from 10 to 30 OC causes a sharpening

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“…More complex models based on spin glass hamiltonians [9] need to introduce "folding funnels" in the energy landscape in order to guide the slow dynamics of a frustrated system [10,11]. The existence of a pathway implies that the bond angles change in a certain order, i.e.…”

mentioning

confidence: 99%

A hierarchical scheme for cooperativity and folding in proteins

Hansen¹,

Jensen²,

Sneppen³

et al. 1998

Physica A: Statistical Mechanics and its Applications

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We propose a protein model based on a hierarchy of constraints that force the protein to follow certain pathways when changing conformation. The model exhibits a first order phase transition, cooperativity and is exactly solvable. It also shows an unexpected symmetry between folding and unfolding pathways as suggested by a recent experiment.Proteins function by switching between different well-defined conformations in the native state. In order to reach the native state the protein has to fold. The number of possible conformations is huge, and the existence of folding pathways guiding the proteins between the relevant conformations seems necessary [1]. The existence of pathways has been experimentally established [2][3][4], but the mechanisms behind these are still to be understood. The free energy difference stabilizing the folded state of a protein, is of the order 20 k B T room for a typical domain consisting of about 100 amino acids, meaning that the binding energy per amino acid is only of order of k B T room [5]. This is a surprisingly small value. The mechanism responsible for stability at very little cost is not known, but has been named "cooperativity" [5].In this letter we propose to model protein folding by a parametrization of the folding pathway. Cooperativity appears in the theory through assuming that only interlocked degrees of freedom are active in the energy window that separate the folded and unfolded states. This also leads to a first order folding transition. Furthermore, the model exhibits an interesting dynamical symmetry when changing conformation. One would expect it to follow the folding pathway in opposite direction when it unfolds. However, under certain conditions it moves in the same direction along the folding pathway both when folding and unfolding. We call this the "mirror effect." This feature of the model is in agreement with recent measurements [6] which suggest this mirror symmetry in the conformational change of albumin at low pH.The amino acids constituting a protein may rotate relative to each other, thus inducing conformational changes in the protein. They furthermore interact. Through changing bond angles, amino acids far apart on the protein may be brought close to each other to form bonds that stabilize a given conformation.Simple models for protein folding which encompass guiding [7] and cooperativity [8] have been proposed. More complex models based on spin glass hamiltonians [9] need to introduce "folding funnels" in the energy landscape in order to guide the slow dynamics of a frustrated system [10,11]. The existence of a pathway implies that the bond angles change in a certain order, i.e. there is a hierarchy among the bond angles themselves. In order to clarify the significance of such a hierarchy, we introduce a model that simultaneously displays a folding pathway, cooperativity and a first order phase transition, thus reproducing three important characteristics of real proteins. The model may be visualized as in Fig. 1. The variables are effective folding angle...

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Protein states and proteinquakes.

Cited by 808 publications

References 35 publications

Multi-basin dynamics of a protein in a crystal environment

Multi-basin dynamics of a protein in a crystal environment

Effect of unfolding on the tryptophanyl fluorescence lifetime distribution in apomyoglobin

A hierarchical scheme for cooperativity and folding in proteins

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