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QAARM: quasi-anharmonic autoregressive model reveals molecular recognition pathways in ubiquitin.

Savol AJ, Burger VM, Agarwal PK, Ramanathan A, Chennubhotla CS - Bioinformatics (2011)

Bottom Line: Molecular dynamics (MD) simulations have dramatically improved the atomistic understanding of protein motions, energetics and function.Observing that such events give rise to long-tailed spatial distributions, we recently developed a higher-order statistics based dimensionality reduction method, called quasi-anharmonic analysis (QAA), for identifying biophysically-relevant reaction coordinates and substates within MD simulations.We show the learned model can be extrapolated to synthesize trajectories of arbitrary length. ramanathana@ornl.gov; chakracs@pitt.edu.

View Article: PubMed Central - PubMed

Affiliation: Joint Carnegie Mellon University-University of Pittsburgh Ph.D. Program in Computational Biology, Department of Computational and Systems Biology, University of Pittsburgh, PA 15260, USA.

ABSTRACT

Motivation: Molecular dynamics (MD) simulations have dramatically improved the atomistic understanding of protein motions, energetics and function. These growing datasets have necessitated a corresponding emphasis on trajectory analysis methods for characterizing simulation data, particularly since functional protein motions and transitions are often rare and/or intricate events. Observing that such events give rise to long-tailed spatial distributions, we recently developed a higher-order statistics based dimensionality reduction method, called quasi-anharmonic analysis (QAA), for identifying biophysically-relevant reaction coordinates and substates within MD simulations. Further characterization of conformation space should consider the temporal dynamics specific to each identified substate.

Results: Our model uses hierarchical clustering to learn energetically coherent substates and dynamic modes of motion from a 0.5 μs ubiqutin simulation. Autoregressive (AR) modeling within and between states enables a compact and generative description of the conformational landscape as it relates to functional transitions between binding poses. Lacking a predictive component, QAA is extended here within a general AR model appreciative of the trajectory's temporal dependencies and the specific, local dynamics accessible to a protein within identified energy wells. These metastable states and their transition rates are extracted within a QAA-derived subspace using hierarchical Markov clustering to provide parameter sets for the second-order AR model. We show the learned model can be extrapolated to synthesize trajectories of arbitrary length.

Contact: ramanathana@ornl.gov; chakracs@pitt.edu.

Show MeSH
Markov diffusion clustering of QAA shows ubiquitin motions involved in binding substrates: The 30 dimensional space determined form QAA is used to construct a set of meta-stable states that are energetically accessible. From a group of 10 000 conformers, we show how the network is modeled with the adjacency matrix C0 shown here. The Markov diffusion produces a total of 78 macro-states at level 4 of the hierarchy. To illustrate the extremum points in the network, we depict two representative clusters (A and B shown in red and green respectively) representing changes within the binding regions of ubiquitin. The primary binding region is indicated by R1.
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Figure 3: Markov diffusion clustering of QAA shows ubiquitin motions involved in binding substrates: The 30 dimensional space determined form QAA is used to construct a set of meta-stable states that are energetically accessible. From a group of 10 000 conformers, we show how the network is modeled with the adjacency matrix C0 shown here. The Markov diffusion produces a total of 78 macro-states at level 4 of the hierarchy. To illustrate the extremum points in the network, we depict two representative clusters (A and B shown in red and green respectively) representing changes within the binding regions of ubiquitin. The primary binding region is indicated by R1.

Mentions: Ubiquitin, a small globular protein, is involved in the proteosomal degradation pathway. It consists of 76 residues and folds into a well defined β-grasp fold. Ubiquitin's structure is evolutionarily conserved across all eukaryotes, consisting of five anti-parallel β-strands (β1−β5) as well as two α-helices. The primary binding surface (R1 in Fig. 3) of ubiquitin is composed of a small number of residues proximal to the flexible β1−β2 and β3−β4 loops. A secondary binding interface consists of the β4−α2 region. Ubiquitin binds to over 300 or more targets in the human cell and naturally has been the focus of many experimental and computational efforts to characterize molecular recognition (Meisenberg et al., 2006). With a large number of crystal structures and NMR conformers available (both substrate-free and substrate-bound), ubiquitin provides an ideal platform for studying protein dynamics in the context of biomolecular recognition.


QAARM: quasi-anharmonic autoregressive model reveals molecular recognition pathways in ubiquitin.

Savol AJ, Burger VM, Agarwal PK, Ramanathan A, Chennubhotla CS - Bioinformatics (2011)

Markov diffusion clustering of QAA shows ubiquitin motions involved in binding substrates: The 30 dimensional space determined form QAA is used to construct a set of meta-stable states that are energetically accessible. From a group of 10 000 conformers, we show how the network is modeled with the adjacency matrix C0 shown here. The Markov diffusion produces a total of 78 macro-states at level 4 of the hierarchy. To illustrate the extremum points in the network, we depict two representative clusters (A and B shown in red and green respectively) representing changes within the binding regions of ubiquitin. The primary binding region is indicated by R1.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3117343&req=5

Figure 3: Markov diffusion clustering of QAA shows ubiquitin motions involved in binding substrates: The 30 dimensional space determined form QAA is used to construct a set of meta-stable states that are energetically accessible. From a group of 10 000 conformers, we show how the network is modeled with the adjacency matrix C0 shown here. The Markov diffusion produces a total of 78 macro-states at level 4 of the hierarchy. To illustrate the extremum points in the network, we depict two representative clusters (A and B shown in red and green respectively) representing changes within the binding regions of ubiquitin. The primary binding region is indicated by R1.
Mentions: Ubiquitin, a small globular protein, is involved in the proteosomal degradation pathway. It consists of 76 residues and folds into a well defined β-grasp fold. Ubiquitin's structure is evolutionarily conserved across all eukaryotes, consisting of five anti-parallel β-strands (β1−β5) as well as two α-helices. The primary binding surface (R1 in Fig. 3) of ubiquitin is composed of a small number of residues proximal to the flexible β1−β2 and β3−β4 loops. A secondary binding interface consists of the β4−α2 region. Ubiquitin binds to over 300 or more targets in the human cell and naturally has been the focus of many experimental and computational efforts to characterize molecular recognition (Meisenberg et al., 2006). With a large number of crystal structures and NMR conformers available (both substrate-free and substrate-bound), ubiquitin provides an ideal platform for studying protein dynamics in the context of biomolecular recognition.

Bottom Line: Molecular dynamics (MD) simulations have dramatically improved the atomistic understanding of protein motions, energetics and function.Observing that such events give rise to long-tailed spatial distributions, we recently developed a higher-order statistics based dimensionality reduction method, called quasi-anharmonic analysis (QAA), for identifying biophysically-relevant reaction coordinates and substates within MD simulations.We show the learned model can be extrapolated to synthesize trajectories of arbitrary length. ramanathana@ornl.gov; chakracs@pitt.edu.

View Article: PubMed Central - PubMed

Affiliation: Joint Carnegie Mellon University-University of Pittsburgh Ph.D. Program in Computational Biology, Department of Computational and Systems Biology, University of Pittsburgh, PA 15260, USA.

ABSTRACT

Motivation: Molecular dynamics (MD) simulations have dramatically improved the atomistic understanding of protein motions, energetics and function. These growing datasets have necessitated a corresponding emphasis on trajectory analysis methods for characterizing simulation data, particularly since functional protein motions and transitions are often rare and/or intricate events. Observing that such events give rise to long-tailed spatial distributions, we recently developed a higher-order statistics based dimensionality reduction method, called quasi-anharmonic analysis (QAA), for identifying biophysically-relevant reaction coordinates and substates within MD simulations. Further characterization of conformation space should consider the temporal dynamics specific to each identified substate.

Results: Our model uses hierarchical clustering to learn energetically coherent substates and dynamic modes of motion from a 0.5 μs ubiqutin simulation. Autoregressive (AR) modeling within and between states enables a compact and generative description of the conformational landscape as it relates to functional transitions between binding poses. Lacking a predictive component, QAA is extended here within a general AR model appreciative of the trajectory's temporal dependencies and the specific, local dynamics accessible to a protein within identified energy wells. These metastable states and their transition rates are extracted within a QAA-derived subspace using hierarchical Markov clustering to provide parameter sets for the second-order AR model. We show the learned model can be extrapolated to synthesize trajectories of arbitrary length.

Contact: ramanathana@ornl.gov; chakracs@pitt.edu.

Show MeSH