Coarse Master Equations for Peptide Folding Dynamics †

Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520, USA.
The Journal of Physical Chemistry B (Impact Factor: 3.3). 06/2008; 112(19):6057-69. DOI: 10.1021/jp0761665
Source: PubMed


We construct coarse master equations for peptide folding dynamics from atomistic molecular dynamics simulations. A maximum-likelihood propagator-based method allows us to extract accurate rates for the transitions between the different conformational states of the small helix-forming peptide Ala5. Assigning the conformational states by using transition paths instead of instantaneous molecular coordinates suppresses the effects of fast non-Markovian dynamics. The resulting master equations are validated by comparing their analytical correlation functions with those obtained directly from the molecular dynamics simulations. We find that the master equations properly capture the character and relaxation times of the entire spectrum of conformational relaxation processes. By using the eigenvectors of the transition rate matrix, we are able to systematically coarse-grain the system. We find that a two-state description, with a folded and an unfolded state, roughly captures the slow conformational dynamics. A four-state model, with two folded and two unfolded states, accurately recovers the three slowest relaxation process with time scales between 1.5 and 7 ns. The master equation models not only give access to the slow conformational dynamics but also shed light on the molecular mechanisms of the helix-coil transition.

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    • "The development of methods that allow the systematic and even automatic clustering is an actively developing area [25,52–57]. Here, we present a method based on the eigenvalue and eigenvector analysis of rate matrices [25] [58] that has the promise to offer a general framework that may be extended from the analysis of relatively small peptides to the folding of larger, more complex proteins. "

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    • "One of these approach is Markov State Modelling in which the kinetics of a molecular system is described by a Markov jump process or Markov chain with the dominant metastable conformations of a molecular system as Markov states [17] [18] [15]. In recent years Markov State Modelling has been applied with striking success to many different molecular systems like peptides including time-resolved spectroscopic experiments [3] [14] [9], proteins and protein folding [5] [11] [2], DNA [8], and ligand-receptor interaction in drug design [7] [4] and more complicated multivalent scenarios [23] [19]. "
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    ABSTRACT: In recent years, Markov state models (MSMs) have attracted a considerable amount of attention with regard to modelling conformation changes and associated function of biomolecular systems. They have been used successfully, e.g. for peptides including time-resolved spectroscopic experiments, protein function and protein folding , DNA and RNA, and ligand-receptor interaction in drug design and more complicated multivalent scenarios. In this article, a novel reweighting scheme is introduced that allows to construct an MSM for certain molecular system out of an MSM for a similar system. This permits studying how molecular properties on long timescales differ between similar molecular systems without performing full molecular dynamics simulations for each system under consideration. The performance of the reweighting scheme is illustrated for simple test cases, including one where the main wells of the respective energy landscapes are located differently and an alchemical transformation of butane to pentane where the dimension of the state space is changed.
    Molecular Physics 11/2014; 113(1):69-78. DOI:10.1080/00268976.2014.944597 · 1.72 Impact Factor
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    • "If proteins bind to larger ligand molecules, e.g. to peptides, other proteins, or DNA or RNA molecules, conformational changes and binding events can be intricately coupled [28– 30]. A promising approach to model such an intricate coupling is Markov state modeling of molecular dynamics simulations [55] [56] [57] [58] [59] [60]. Such Markov state modeling has been previously applied to obtain pathways for the conformational changes of proteins [61] [62] [63] [64]. "
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