Forced unfolding of fibronectin type 3 modules: an analysis by biased molecular dynamics simulations

Paci, Emanuele; Karplus, Martin

doi:10.1006/jmbi.1999.2670

Cited by 324 publications

(344 citation statements)

References 52 publications

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“…Ensemble refinement against both NOEs and order parameters was achieved using biased molecular dynamics (Paci & Karplus, 1999) and a simulated annealing protocol starting from an x-ray structure of ubiquitin (Vijay- Kumar et al 1987). Cross-validation of the ensemble was performed by comparing values computed from the ensemble to experimental RDCs and 3 J couplings that were excluded from the ensemble refinement process.…”

Section: Ensemble Approaches For Analyzing Protein Dynamicsmentioning

confidence: 99%

Protein dynamics and function from solution state NMR spectroscopy

Kovermann

Rogne

Wolf‐Watz

2016

Quart. Rev. Biophys.

145

122

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Abstract. It is well-established that dynamics are central to protein function; their importance is implicitly acknowledged in the principles of the Monod, Wyman and Changeux model of binding cooperativity, which was originally proposed in 1965. Nowadays the concept of protein dynamics is formulated in terms of the energy landscape theory, which can be used to understand protein folding and conformational changes in proteins. Because protein dynamics are so important, a key to understanding protein function at the molecular level is to design experiments that allow their quantitative analysis. Nuclear magnetic resonance (NMR) spectroscopy is uniquely suited for this purpose because major advances in theory, hardware, and experimental methods have made it possible to characterize protein dynamics at an unprecedented level of detail. Unique features of NMR include the ability to quantify dynamics (i) under equilibrium conditions without external perturbations, (ii) using many probes simultaneously, and (iii) over large time intervals. Here we review NMR techniques for quantifying protein dynamics on fast (ps-ns), slow (μs-ms), and very slow (s-min) time scales. These techniques are discussed with reference to some major discoveries in protein science that have been made possible by NMR spectroscopy.

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Section: Ensemble Approaches For Analyzing Protein Dynamicsmentioning

confidence: 99%

Protein dynamics and function from solution state NMR spectroscopy

Kovermann

Rogne

Wolf‐Watz

2016

Quart. Rev. Biophys.

145

122

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“…An alternative method is transition path sampling [23], which develops MC specific procedures to produce a set of reactive trajectories describing the dynamical pathways that bridge stable states. Methods for computing conformational transitions have also been developed based on biased or targeted MD [24,25] and on normal mode analysis [26]. Finally mention a category of methods, including the lid algorithm [27] (for discrete spaces) and the threshold algorithm [28] (for continuous spaces), originally devoted to explore exhaustively the regions around a given set of energy minima, and which, by extension, are able to characterize conformational transitions between minima without prior information about their connectivity.…”

Section: Introductionmentioning

confidence: 99%

Randomized tree construction algorithm to explore energy landscapes

et al. 2011

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We report in the present work a new method for exploring conformational energy landscapes. The method, called T-RRT, combines ideas from statistical physics and robot path planning algorithms. A search tree is constructed on the conformational space starting from a given state. The tree expansion is driven by a double strategy: on the one hand, it is naturally biased towards yet unexplored regions of the space; on the other, a Monte Carlo-like transition test guides the expansion toward energetically favorable regions. The balance between these two strategies is automatically achieved thanks to a self-tuning mechanism. The method is able to efficiently find both, energy minima and transition paths between them. As a proof of concept, the method is applied to two academic benchmarks and to the alanine dipeptide.

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“…Single-molecule manipulation with an atomic force microscope (AFM) (5)(6)(7)(8)(9), laser tweezer stretching (10), and analogous computer experiments pioneered by Schulten and coworkers (11)(12)(13) have revealed details about unfolding and unbinding events of individual proteins and their complexes. In an AFM experiment, a molecule is subjected to a time-varying external force, for instance by pulling on the end of a linear polymer (Fig.…”

mentioning

confidence: 99%

Free energy reconstruction from nonequilibrium single-molecule pulling experiments

Hummer

Szabó

2001

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

856

862

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Laser tweezers and atomic force microscopes are increasingly used to probe the interactions and mechanical properties of individual molecules. Unfortunately, using such time-dependent perturbations to force rare molecular events also drives the system away from equilibrium. Nevertheless, we show how equilibrium free energy profiles can be extracted rigorously from repeated nonequilibrium force measurements on the basis of an extension of Jarzynski's remarkable identity between free energies and the irreversible work.R ecent advances in the micromanipulation of single molecules have led to new insights into the dynamics, interactions, structure, and mechanical properties of individual molecules (1-4). Single-molecule manipulation with an atomic force microscope (AFM) (5-9), laser tweezer stretching (10), and analogous computer experiments pioneered by Schulten and coworkers (11-13) have revealed details about unfolding and unbinding events of individual proteins and their complexes. In an AFM experiment, a molecule is subjected to a time-varying external force, for instance by pulling on the end of a linear polymer (Fig. 1). The applied force is determined from the time-dependent position of the cantilever tip with respect to the sample. Thus, one can drive rare molecular events (14), determine their force characteristics, and simultaneously monitor them with atomic resolution. However, both experiments and simulations actively perturb the system, leading to hysteresis and nonequilibrium effects.How can one extract equilibrium properties from such measurements that drive the system away from equilibrium (15, 16)? From the second law of thermodynamics, we know that on average, the mechanical work of pulling will be larger than the free energy. Only if the experiment is performed reversibly, i.e., infinitely slowly, will the work equal the free energy. Thus, making rigorous thermodynamic measurements by pulling appears to require an extrapolation to zero pulling speed. However, Jarzynski (17, 18) recently discovered a remarkable identity between thermodynamic free energy differences and the irreversible work, thus extending the inequality of the second law of thermodynamics. This identity, although not directly applicable to atomic force measurements, suggests that in principle one should be able to extract free energy surfaces from repeated pulling experiments. In this paper, we show how this can be done in practice.Theory. We begin by showing that Jarzynski's identity follows almost immediately from the Feynman-Kac theorem for path integrals (19). This derivation leads directly to the appropriate extension, which forms the basis for the solution of the free energy reconstruction problem. This extension has been obtained by Crooks (20) as a special case of an even more general relation between forward and backward path averages. Consider a system whose phase-space density evolves according to a Liouville-type equation: Ѩf͑x, t͒Ѩt ϭ ᏸ t f͑x, t͒.[1]ᏸ t is an explicitly time-dependent evolution operator that has the ...

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Forced unfolding of fibronectin type 3 modules: an analysis by biased molecular dynamics simulations

Cited by 324 publications

References 52 publications

Protein dynamics and function from solution state NMR spectroscopy

Protein dynamics and function from solution state NMR spectroscopy

Randomized tree construction algorithm to explore energy landscapes

Free energy reconstruction from nonequilibrium single-molecule pulling experiments

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