Computing the transition state populations in simple protein models

Ozkan, S. Banu; Dill, Ken A.; Bahar, İvet

doi:10.1002/bip.10280

Cited by 51 publications

(45 citation statements)

References 24 publications

(17 reference statements)

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“…A second approach pursues a severe discretization of conformation-state space that enables the use of masterequation stochastic kinetics (30)(31)(32). Although an exact kinetic description can be obtained, a comprehensive and accurate discretization of configuration space is required.…”

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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.

123

165

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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.

123

165

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“…The resulting scheme can be represented as a graph or network (26). The kinetics on this graph is assumed to be stochastic, leading to a Markovian model for the time dependence of the populations of the various states (10,11,(27)(28)(29)(30). This approach is particularly well suited for reduced lattice models (10, 11).…”

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confidence: 99%

Protein folding pathways from replica exchange simulations and a kinetic network model

Andrec

Felts

Gallicchio

et al. 2005

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

140

167

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We present an approach to the study of protein folding that uses the combined power of replica exchange simulations and a network model for the kinetics. We carry out replica exchange simulations to generate a large (Ϸ10 6 ) set of states with an all-atom effective potential function and construct a kinetic model for folding, using an ansatz that allows kinetic transitions between states based on structural similarity. We use this network to perform random walks in the state space and examine the overall network structure. Results are presented for the C-terminal peptide from the B1 domain of protein G. The kinetics is two-state after small temperature perturbations. However, the coil-to-hairpin folding is dominated by pathways that visit metastable helical conformations. We propose possible mechanisms for the ␣-helix͞ ␤-hairpin interconversion.graph ͉ master equation ͉ protein G P rotein folding is a fundamental problem in modern structural biology, and recent advances in experimental techniques have helped to elucidate some of the thermodynamic and kinetic features that underlie different stages of the folding process (1-3). Computer simulations using reduced (4-11) and atomistic molecular models (12-21) have played a central role in the interpretation of experimental studies. Although reduced models have provided considerable insight into the overall mechanisms of protein folding, especially in helping to clarify the nature of folding funnels, intermediates, and kinetic bottlenecks, they are limited in their ability to explore the detailed molecular aspects of folding. However, because of the large number of degrees of freedom and the rarity of folding events even in small model systems, all-atom simulations require both considerable computational resources and ingenuity to obtain meaningful results; a variety of methods have been developed to increase simulation efficiency.A particularly powerful technique for the calculation of free energy surfaces and other thermodynamic properties of complex systems is replica exchange molecular dynamics (REMD) (22), in which a generalized ensemble of the system is simulated in parallel over a range of temperatures. Periodically, coordinates are exchanged by using a Metropolis criterion that ensures that at any given temperature a canonical distribution is realized and allows for more efficient barrier crossing than could be obtained with conventional simulation methods. Although REMD is a powerful method for exploring free energy landscapes, it does not provide direct information about kinetics. To study folding by using all-atom effective potentials, heterogeneous distributed computing (16,19) and transition path sampling (23, 24) techniques have been used. Although the former can enhance sampling by combining information from a large number of short MD trajectories ''steered'' by rare events, these techniques can introduce a bias toward fast events in the ensemble average of the reactive trajectories (25). Transition path sampling (23,24) can yield quantitative estimat...

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“…After examining the enthalpies and entropies for the formation for all the possible different base stacks, we find that there are two on-pathway rate-limiting steps corresponding to the formation of the native stacks (3,4,18,19) = (U,C,G,A) and (5,6,16,17) = (G,A,U,C), respectively, and two off-pathway rate-limiting steps, corresponding to the disrupting of the non-native stacks (5,6,11,12) = (G,A,U,C), and (11,12,18,19) = (U,C,G,A). According to these rate-limiting steps, the conformation space can be classified into the following seven clusters: cluster 1 for the 586 conformations without any of the four stacks formed, cluster 2 for the 105 conformations with stack (3,4,18,19), cluster 3 for the 51 conformations with stack (5,6,11,12), cluster 4 for the 76 conformations with stack (5,6,16,17), cluster 5 for the 36 conformations with stack (11,12,18,19), cluster 6 for the five conformations with both stacks (3,4,18,19) and (5,6,11,12), and cluster 7 for the 20 conformations with both stacks (3,4,18,19) and (5,…”

Section: Application To Realistic Rna Folding Kineticsmentioning

confidence: 99%

“…According to these rate-limiting steps, the conformation space can be classified into the following seven clusters: cluster 1 for the 586 conformations without any of the four stacks formed, cluster 2 for the 105 conformations with stack (3,4,18,19), cluster 3 for the 51 conformations with stack (5,6,11,12), cluster 4 for the 76 conformations with stack (5,6,16,17), cluster 5 for the 36 conformations with stack (11,12,18,19), cluster 6 for the five conformations with both stacks (3,4,18,19) and (5,6,11,12), and cluster 7 for the 20 conformations with both stacks (3,4,18,19) and (5,6,16,17). The native state is in cluster 7, the fully unfolded state is in cluster 1, and there are three misfolded traps: cluster 3, 5 and 6.…”

Section: Application To Realistic Rna Folding Kineticsmentioning

confidence: 99%

“…The above rate matrix has the following eigenvalues in the increasing order: (16) Using the eigenvector analysis, 17 we can identify the kinetic modes for each of the eigenvalues. For example, the lowest nonzero eigenvalue λ 1 corresponds to the intercluster transition 5→1 for the detrapping of the stack (11,12,18,19), λ 2 corresponds to the detrapping of stack (5,6,11,12), and λ 3 corresponds to the formation of the on-pathway rate-limiting stacks (3,4,18,19) and (5,6,16,17). From the rate matrix, we can also estimate fractional population for each pathway starting from cluster 1.…”

Section: Application To Realistic Rna Folding Kineticsmentioning

confidence: 99%

See 1 more Smart Citation

Analyzing the biopolymer folding rates and pathways using kinetic cluster method

Zhang

Chen

2003

The Journal of Chemical Physics

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A kinetic cluster method enables us to analyze biopolymer folding kinetics with discrete rate-limiting steps by classifying biopolymer conformations into pre-equilibrated clusters. The overall folding kinetics is determined by the intercluster transitions. Due to the complex energy landscapes of biopolymers, the intercluster transitions have multiple pathways and can have kinetic intermediates (local free-energy minima) distributed on the intercluster pathways. We focus on the RNA secondary structure folding kinetics. The dominant folding pathways and the kinetic partitioning mechanism can be identified and quantified from the rate constants for different intercluster pathways. Moreover, the temperature dependence of the folding rate can be analyzed from the interplay between the stabilities of the on-pathway (nativelike) and off-pathway (misfolded) conformations and from the kinetic partitioning between different intercluster pathways. The predicted folding kinetics can be directly tested against experiments.

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Computing the transition state populations in simple protein models

Cited by 51 publications

References 24 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

Protein folding pathways from replica exchange simulations and a kinetic network model

Analyzing the biopolymer folding rates and pathways using kinetic cluster method

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