Stochastic Path Approach to Compute Atomically Detailed Trajectories:  Application to the Folding of C Peptide

Elber, Ron; Meller, Jarosław; Olender, Roberto

doi:10.1021/jp983774z

Cited by 101 publications

(89 citation statements)

References 28 publications

(70 reference statements)

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“…Path sampling approaches (5)(6)(7)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42) can, in principle, employ models of any level of detail, without approximation to the correct statistical mechanics. The potential for efficiency in these approaches stems from an extreme separation of time scales: rare events are rare because they are infrequent, not because the events are slow.…”

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confidence: 99%

Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin

Zhang

Jasnow

Zuckerman

2007

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

120

163

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The computational sampling of rare, large-scale, conformational transitions in proteins is a well appreciated challenge-for which a number of potentially efficient path-sampling methodologies have been proposed. Here, we study a large-scale transition in a united-residue model of calmodulin using the ''weighted ensemble'' (WE) approach of Huber and Kim. Because of the model's relative simplicity, we are able to compare our results with bruteforce simulations. The comparison indicates that the WE approach quantitatively reproduces the brute-force results, as assessed by considering (i) the reaction rate, (ii) the distribution of event durations, and (iii) structural distributions describing the heterogeneity of the paths. Importantly, the WE method is readily applied to more chemically accurate models, and by studying a series of lower temperatures, our results suggest that the WE method can increase efficiency by orders of magnitude in more challenging systems.transition path ͉ path sampling ͉ weighted ensemble ͉ conformational transition

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mentioning

confidence: 99%

Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin

Zhang

Jasnow

Zuckerman

2007

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

120

163

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“…The structural properties of the transition state ensemble can then be determined by sampling the thermal distribution of states in the dominant free energy barrier rather than by making ''kinetic'' measurements (e.g., measuring folding rates and transmission coefficients, or simulating complete folding pathways). The elimination of these kinetic measurements allows the folding transition state to be rapidly computed (compared with alternate methods), especially in large and complex systems (31)(32)(33)(34)(35) that cannot be studied by other means (29,(36)(37)(38)(39).…”

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confidence: 99%

Landscape approaches for determining the ensemble of folding transition states: Success and failure hinge on the degree of frustration

Nymeyer

Socci

Onuchic

2000

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

111

110

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We present a method for determining structural properties of the ensemble of folding transition states from protein simulations. This method relies on thermodynamic quantities (free energies as a function of global reaction coordinates, such as the percentage of native contacts) and not on ''kinetic'' measurements (rates, transmission coefficients, complete trajectories); consequently, it requires fewer computational resources compared with other approaches, making it more suited to large and complex models. We explain the theoretical framework that underlies this method and use it to clarify the connection between the experimentally determined ⌽ value, a quantity determined by the ratio of rate and stability changes due to point mutations, and the average structure of the transition state ensemble. To determine the accuracy of this thermodynamic approach, we apply it to minimalist protein models and compare these results with the ones obtained by using the standard experimental procedure for determining ⌽ values. We show that the accuracy of both methods depends sensitively on the amount of frustration. In particular, the results are similar when applied to models with minimal amounts of frustration, characteristic of rapid-folding, single-domain globular proteins.protein folding ͉ ⌽ values ͉ folding funnels ͉ folding landscapes E nergy landscape theory and the funnel concept have provided a theoretical framework for understanding protein folding (1-7), which is an alternative to the earlier idea that there is a single pathway for the folding event comprising uniquely defined structural intermediates (8,9). The connection between the landscape theory and real proteins is best established in the context of small fast folding proteins, which fold on millisecond time scales and have a single folding domain; i.e., they are two-state folders with a single, well defined funnel (10). In addition to the theoretical literature describing this theory and its applications (see, for example, the citations above, refs. 5 and 6, and references therein), a new generation of clever experiments [NMR dynamic spectroscopy, protein engineering, laser initiated folding, and ultrafast mixing (see, for example, refs. 11-27)] are providing the temporal and spatial detail needed to extend and elaborate on it.A central result of this theory is that proteins with funneled landscapes have population dynamics that can be understood as the diffusion of an ensemble of configurations over a lowdimensional free energy surface (1, 3, 4). This energy surface may be constructed by using many different order parameters. The primary requirements are that they distinguish native-like and non-native-like structures and that they group together conformations with similar energies; ¶ i.e., the dispersion in energies of states with similar values of these parameters is small. Many simple order parameters that are computationally convenient, like the number of tertiary contacts Q, or experimentally convenient, like the radius of gyration, satisfy these r...

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“…These trajectories can probe if the dynamics progresses as expected from the equilibration assumption inherent to the PMF calculations ͑i.e., to probe whether the choice of the reaction coordinate as the slowest order parameter was appropriate, 115 or if coupling to other degrees of freedom is significant 116,117 ͒. Because transition path sampling is a method that does not require the definition of a reaction coordinate, the ensembles of dynamical transition trajectories generated by it ͑or by other longtime dynamical methods [118][119][120][121][122][123] ͒ can be grouped together and further analyzed to obtain information about distinct reaction pathways.…”

Section: Concluding Discussionmentioning

confidence: 99%

An experimentally guided umbrella sampling protocol for biomolecules

Mills

Andricioaei

2008

The Journal of Chemical Physics

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We present a simple method for utilizing experimental data to improve the efficiency of numerical calculations of free energy profiles from molecular dynamics simulations. The method involves umbrella sampling simulations with restraining potentials based on a known approximate estimate of the free energy profile derived solely from experimental data. The use of the experimental data results in optimal restraining potentials, guides the simulation along relevant pathways, and decreases overall computational time. In demonstration of the method, two systems are showcased. First, guided, unguided ͑regular͒ umbrella sampling simulations and exhaustive sampling simulations are compared to each other in the calculation of the free energy profile for the distance between the ends of a pentapeptide. The guided simulation use restraints based on a simulated "experimental" potential of mean force of the end-to-end distance that would be measured by fluorescence resonance energy transfer ͑obtained from exhaustive sampling͒. Statistical analysis shows a dramatic improvement in efficiency for a 5 window guided umbrella sampling over 5 and 17 window unguided umbrella sampling simulations. Moreover, the form of the potential of mean force for the guided simulations evolves, as one approaches convergence, along the same milestones as the extensive simulations, but exponentially faster. Second, the method is further validated by replicating the forced unfolding pathway of the titin I27 domain using guiding umbrella sampling potentials determined from actual single molecule pulling data. Comparison with unguided umbrella sampling reveals that the use of guided sampling encourages unfolding simulations to converge faster to a forced unfolding pathway that agrees with previous results and produces a more accurate potential of mean force.

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Stochastic Path Approach to Compute Atomically Detailed Trajectories: Application to the Folding of C Peptide

Cited by 101 publications

References 28 publications

Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin

Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin

Landscape approaches for determining the ensemble of folding transition states: Success and failure hinge on the degree of frustration

An experimentally guided umbrella sampling protocol for biomolecules

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