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RNA Structure Large ribosome subunit -- Chain0: 2914 bases -- Chain9: 122 bases
Citation preview
Forward and inverse kinematics in RNA
backbone conformations
By Xueyi Wang and Jack Snoeyink
Department of Computer ScienceUNC-Chapel Hill
Outline RNA Structure &
Crystallography Ramachandran-like plots Measurements and Conformations Forward and Inverse Kinematics Future Work
RNA Structure
Large ribosome subunit
-- Chain0: 2914 bases
-- Chain9: 122 bases
RNA StructureResidue
Suite
α
βγ
δ
εζ
δγ β
αζ
δε
RNA Structure & Crystallography
Large RNA structures at 2.5 or 3Å resolution are considered good.
Electron Density Map--The Phosphates and Bases can be clearly
located.--Sugar puckers can be derived.--Other parts are ambiguous. Goal: Achieve correct RNA structures from
electron density maps.
Electron Density Map
Image Courtesy Richardsons’ Lab
All-Atom Contact Analysis
Image Courtesy Richardsons’ Lab
Complexity of RNA Backbone
α
β
γδε
ζ
Nucleic Acid:6 dihedrals
Amino Acid:2 dihedrals
φ
ψ
ψ
Cα
Cα
φ
φ
Complexity of RNA Backbone
RNA Backbone:Two ends and the base plane are fixed
Protein Side-chain:One end is fixed
α
β
γδε
ζ
Outline RNA Structure & Crystallography Ramachandran-like plots Measurements and Conformations Forward and Inverse Kinematics Future Work
Ramachandran Plot
φ
ψ
ψ
Cα
Cα
φ
φ
L. Murray, et al. PNAS:2003
99% backbone steric clashes are within suites
42 Conformations A-form RNA
accounts for 75% data
Observed Data
Space-filling Model forRNA Residue/Suite
Standard RNA structure parameters --From NDB (Nucleic Acid Database) Dihedrals are sampled at every 5°. Overlaps (distances of pairs of atoms
that are at least four bonds apart): --No Clash: > vdwi + vdwj - 0.2Å --Small Clash: < vdwi + vdwj - 0.2Å and > vdwi + vdwj - 0.5Å --Bad Clash: < vdwi + vdwj - 0.5Å
Valid Ranges of Dihedrals
Distribution of δ(Bimodal): Space-filling Model: -- C3’endo: [65°, 94°] -- C2’endo: [117°, 167°] Observed Data (L. Murray, et al. PNAS:2003) -- C3’endo: near 84°. -- C2’endo: near 147°.
δ
Valid Ranges of Dihedrals
Distribution of ε (Eclipsed): Space-filling Model: -- C3’endo: [-180°, -30°] [160°, 180°] whenδ=94° [-180°, -70°] [115°, 180°] whenδ=65° -- C2’endo: [-185°, -55°] whenδ=117° [-175°, -55°] whenδ=167° Observed Data (L. Murray, et al. PNAS:2003) -- C3’endo: mode=-150° -- C2’endo: mode=-100°.
δ
ε
Valid Ranges of Dihedrals
Distribution of ζ,α,β and γ: Space-filling Model: -- Peaks of ζ and α: p, m and t. -- Peaks of β: t. -- Peaks of γ: mode=t. Observed Data (L. Murray, et al. PNAS:2003) -- Peaks of ζ: p, m, t and -140 (only in C3’endo). -- Peaks of α: p, m, t and -110 (only in C3’endo). -- Peaks of β: t, 110, -135 and 135 and 80 (only in
C3’endo). -- Peaks of γ: p, m and t.
αβγδε
ζ
Demo δ-ε-ζ plots (and clash plots): -- C3’endo -- C2’endo α-β-γ plots: -- C3’endo -- C2’endo
Outline RNA Structure & Crystallography Ramachandran-like plots Measurements and
Conformations Forward and Inverse Kinematics Future Work
L. Murray, et al. PNAS:2003
99% backbone steric clashes are within suites
42 Conformations A-form RNA
accounts for 75% data
Observed Data
Measurements Known information in electron density
map: -- Phosphate positions -- base plane positions Goals: --Map the known positions to C3’endo and C2’endo puckers. --Map the known positions to 42 conformations.
Measurements
18 measurements -- distances: N1--N2, P--N1, etc. -- perpendicular distances: P -- C1-N1, P -- Sugar
Pucker -- angles: N1--P--N2, P--N1--N2, etc.
C1
N1 N2
C2
P
Criteria The measurement should well separate the C3’ endo
and C2’ endo puckers. The span of the measurement (SPANall) should be a
long range (>2Å or >60°). The ratio of the span of each conformation
measurement to the span of the whole value (SPANeach / SPANall or ΣSPANeach / SPANall) should be small.
The overlapping among different conformations should be small.
The overlapping of all SPANeach should cover the SPANall (i.e. no gaps).
Separate Sugar Puckers Space-filling Model: -- C3’endo: P -- N1-C1 > 2.537Å -- C2’endo: P -- N1-C1 < 2.313Å Proposed measurement from
Richardson’s lab: -- C3’endo: P -- First Base Plane > 2.9Å -- C2’endo: P -- First Base Plane < 2.9Å
Separate 42 Conformations
All 42 conformations -- (P--Sugar2, N1--N2 and P--N1--N2) and (P--Sugar2, C1--C2
and P--C1--C2). Conformations in the different sugar puckers -- C3’endo and C3’endo: (P--Sugar2, N1--N2 and P--N2--N1). -- C3’endo and C2’endo: (P--Sugar2, N1--N2 and P--N2--N1). -- C2’endo and C3’endo: (P--Sugar2, N1--N2 and P--N2). -- C2’endo and C2’endo: (P--Sugar2, N1--N2 and P--N2).
Outline RNA Structure & Crystallography Ramachandran-like plots Measurements and Conformations Forward and Inverse Kinematics Future Work
Electron Density Map
Image Courtesy Richardsons’ Lab
Forward and Inverse Kinematics
Forward Kinematics: -- One end is fixed. -- Fit some constraints. Inverse Kinematics: -- Both ends are fixed. -- At least 6 degrees of freedom.
Forward Kinematics
Start from phosphate. Fit bases.
Forward Kinematics
Start from base. Fit phosphates.
Inverse Kinematics
Start from two phosphates. Fit the sugar pucker.
Inverse Kinematics
Start from two bases. Fit the phosphate position.
Problems Too many degrees of freedoms. -- Use Ramachandran-like plots and the relations of
measurements and conformations to reduce the choices. Each phosphorus or sugar pucker will be used
two times. -- Keep several valid conformations calculated by forward
or inverse kinematics in each residue and suite. -- Merge the phosphorus or sugar pucker calculated from
adjacent residues or suites using the combination of the valid conformations.
Example: Solve Existing Bad Clashes
Forward Kinematics: Start from phosphorus and fits the bases.
Solve the bad clashes in the existing RNA structures.
-- Fix the atoms outside the suite and the base planes.
-- Do forward kinematics in two directions and meet all the constraints (bond lengths, angles, etc.).
-- Choose for no bad clash conformations. -- Do small adjustments if necessary.
Example: Solve Existing Bad Clashes
Suite 101 (residue 100 and 101) in ar0001.pdb Suite 50 (residue 59 and 60) in 1YFG.pdb
Improvements
Extend the forward kinematics to two residues. Solve slightly bad clashes (<vdwi+vdwj-0.4 and
>vdwi+vdwj-0.5) by wiggling atom positions.
Outline RNA Structure & Crystallography Ramachandran-like plots Measurements and Conformations Inverse and Forward Kinematics Future Work
Ramachandran-like plots
Find some good methods to project the 6D (in residue) and 7D (in suite) data into visible plots.
Analyze the collision boundaries between valid and invalid conformations.
Measurements and Conformations
Refine the relations of measurements and conformations.
Use the relations of measurements and conformations to accelerate the process of determining RNA structure.
Forward and Inverse Kinematics
Resolve bad clashes in existing RNA structures.
Build automatic tools to determine the RNA structures from electron density maps.
Acknowledgements:-- Prof. Jane Richardson, Prof. David
Richardson and Laura Murray.-- NSF grant 0076984.
The End