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Characterizing RNA ensembles from NMR data with kinematic models.

Fonseca R, Pachov DV, Bernauer J, van den Bedem H - Nucleic Acids Res. (2014)

Bottom Line: We found that KGSrna ensembles accurately represent the conformational landscapes of 3D RNA encoded by NMR proton chemical shifts.KGSrna resolves motionally averaged NMR data into structural contributions; when coupled with residual dipolar coupling data, a KGSrna ensemble revealed a previously uncharacterized transient excited state of the HIV-1 trans-activation response element stem-loop.Ensemble-based interpretations of averaged data can aid in formulating and testing dynamic, motion-based hypotheses of functional mechanisms in RNAs with broad implications for RNA engineering and therapeutic intervention.

View Article: PubMed Central - PubMed

Affiliation: AMIB Project, INRIA Saclay-Île de France, 1 rue Honoré d'Estienne d'Orves, Bâtiment Alan Turing, Campus de l'École Polytechnique, 91120 Palaiseau, France Laboratoire d'Informatique de l'École Polytechnique (LIX), CNRS UMR 7161, École Polytechnique, 91128 Palaiseau, France Department of Computer Science, University of Copenhagen, Nørre Campus, Universitetsparken 5, DK-2100 Copenhagen, Denmark.

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Kinematic representation of RNA. (a) A single nucleotide of RNA with its torsional degrees-of-freedom. (b) Edges in the directed spanning tree encode n torsional degrees-of-freedom  and vertices (circles) encode rigid bodies. Pentagons represent riboses, which have an additional internal degree-of-freedom governing their conformation (puckering). The hydrogen bond h-A closes a kinematic cycle, and is one of m distance constraints. As the position of the hydrogen atom h changes through perturbation of dihedral angles in the left branch of the tree, the new position of h should be matched by appropriate changes in the right branch, i.e. . Similarly, a change in position of heavy atom A from the right tree should be matched by changes in the left tree. These instantaneous distance constraints define the 6m × n Jacobian matrix . (c) A schematic representation of the subspace of conformational space defined by the closure constraints. The subspace (blue surface) is highly nonlinear, but can be locally approximated by its tangent space, the -space of  (translucent blue plane).
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Figure 1: Kinematic representation of RNA. (a) A single nucleotide of RNA with its torsional degrees-of-freedom. (b) Edges in the directed spanning tree encode n torsional degrees-of-freedom and vertices (circles) encode rigid bodies. Pentagons represent riboses, which have an additional internal degree-of-freedom governing their conformation (puckering). The hydrogen bond h-A closes a kinematic cycle, and is one of m distance constraints. As the position of the hydrogen atom h changes through perturbation of dihedral angles in the left branch of the tree, the new position of h should be matched by appropriate changes in the right branch, i.e. . Similarly, a change in position of heavy atom A from the right tree should be matched by changes in the left tree. These instantaneous distance constraints define the 6m × n Jacobian matrix . (c) A schematic representation of the subspace of conformational space defined by the closure constraints. The subspace (blue surface) is highly nonlinear, but can be locally approximated by its tangent space, the -space of (translucent blue plane).

Mentions: The value of analyzing NMR spectroscopy data guided by a conformational ensemble has long been recognized (14,15). Conformational diversity for RNA ensemble analyses is often provided by sophisticated molecular dynamics simulations (16,17). Long trajectories with specialized force fields on dedicated supercomputers are required to adequately sample conformational space, limiting ensemble analyses to modestly-sized RNA molecules (18). Here, we present an efficient conformational sampling procedure, Kino-geometric sampling for RNA (KGSrna), which can report on ensembles of RNA molecular conformations orders of magnitude faster than MD simulations. KGSrna represents an RNA molecule with rotatable, single bonds as degrees-of-freedom and groups of atoms as rigid bodies (Figure 1a). In this representation, non-covalent bonds form distance constraints, which create nested, closed rings (Figure 1b). Torsional degrees-of-freedom in a closed ring demand carefully coordinated changes to avoid breaking the non-covalent bond, which greatly reduces the conformational flexibility (19–22). The reduced flexibility from a network of nested, closed rings consequently deforms the biomolecule along preferred directions on the conformational landscape. In contrast to techniques based on explicit constraint counting (19,22), our new procedure projects degrees-of-freedom onto a lower-dimensional subspace of conformation space, in which the geometries of the non-covalent bonds are maintained exactly under conformational perturbation.


Characterizing RNA ensembles from NMR data with kinematic models.

Fonseca R, Pachov DV, Bernauer J, van den Bedem H - Nucleic Acids Res. (2014)

Kinematic representation of RNA. (a) A single nucleotide of RNA with its torsional degrees-of-freedom. (b) Edges in the directed spanning tree encode n torsional degrees-of-freedom  and vertices (circles) encode rigid bodies. Pentagons represent riboses, which have an additional internal degree-of-freedom governing their conformation (puckering). The hydrogen bond h-A closes a kinematic cycle, and is one of m distance constraints. As the position of the hydrogen atom h changes through perturbation of dihedral angles in the left branch of the tree, the new position of h should be matched by appropriate changes in the right branch, i.e. . Similarly, a change in position of heavy atom A from the right tree should be matched by changes in the left tree. These instantaneous distance constraints define the 6m × n Jacobian matrix . (c) A schematic representation of the subspace of conformational space defined by the closure constraints. The subspace (blue surface) is highly nonlinear, but can be locally approximated by its tangent space, the -space of  (translucent blue plane).
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4150802&req=5

Figure 1: Kinematic representation of RNA. (a) A single nucleotide of RNA with its torsional degrees-of-freedom. (b) Edges in the directed spanning tree encode n torsional degrees-of-freedom and vertices (circles) encode rigid bodies. Pentagons represent riboses, which have an additional internal degree-of-freedom governing their conformation (puckering). The hydrogen bond h-A closes a kinematic cycle, and is one of m distance constraints. As the position of the hydrogen atom h changes through perturbation of dihedral angles in the left branch of the tree, the new position of h should be matched by appropriate changes in the right branch, i.e. . Similarly, a change in position of heavy atom A from the right tree should be matched by changes in the left tree. These instantaneous distance constraints define the 6m × n Jacobian matrix . (c) A schematic representation of the subspace of conformational space defined by the closure constraints. The subspace (blue surface) is highly nonlinear, but can be locally approximated by its tangent space, the -space of (translucent blue plane).
Mentions: The value of analyzing NMR spectroscopy data guided by a conformational ensemble has long been recognized (14,15). Conformational diversity for RNA ensemble analyses is often provided by sophisticated molecular dynamics simulations (16,17). Long trajectories with specialized force fields on dedicated supercomputers are required to adequately sample conformational space, limiting ensemble analyses to modestly-sized RNA molecules (18). Here, we present an efficient conformational sampling procedure, Kino-geometric sampling for RNA (KGSrna), which can report on ensembles of RNA molecular conformations orders of magnitude faster than MD simulations. KGSrna represents an RNA molecule with rotatable, single bonds as degrees-of-freedom and groups of atoms as rigid bodies (Figure 1a). In this representation, non-covalent bonds form distance constraints, which create nested, closed rings (Figure 1b). Torsional degrees-of-freedom in a closed ring demand carefully coordinated changes to avoid breaking the non-covalent bond, which greatly reduces the conformational flexibility (19–22). The reduced flexibility from a network of nested, closed rings consequently deforms the biomolecule along preferred directions on the conformational landscape. In contrast to techniques based on explicit constraint counting (19,22), our new procedure projects degrees-of-freedom onto a lower-dimensional subspace of conformation space, in which the geometries of the non-covalent bonds are maintained exactly under conformational perturbation.

Bottom Line: We found that KGSrna ensembles accurately represent the conformational landscapes of 3D RNA encoded by NMR proton chemical shifts.KGSrna resolves motionally averaged NMR data into structural contributions; when coupled with residual dipolar coupling data, a KGSrna ensemble revealed a previously uncharacterized transient excited state of the HIV-1 trans-activation response element stem-loop.Ensemble-based interpretations of averaged data can aid in formulating and testing dynamic, motion-based hypotheses of functional mechanisms in RNAs with broad implications for RNA engineering and therapeutic intervention.

View Article: PubMed Central - PubMed

Affiliation: AMIB Project, INRIA Saclay-Île de France, 1 rue Honoré d'Estienne d'Orves, Bâtiment Alan Turing, Campus de l'École Polytechnique, 91120 Palaiseau, France Laboratoire d'Informatique de l'École Polytechnique (LIX), CNRS UMR 7161, École Polytechnique, 91128 Palaiseau, France Department of Computer Science, University of Copenhagen, Nørre Campus, Universitetsparken 5, DK-2100 Copenhagen, Denmark.

Show MeSH
Related in: MedlinePlus