Predicting Coaxial Stacking by Free Energy Minimization
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Transcript of Predicting Coaxial Stacking by Free Energy Minimization
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Predicting Coaxial Stacking by Free
Energy Minimization
David Mathews
Department of Biochemistry & Biophysics
University of Rochester Medical Center
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Predicting Coaxial Stacking:
• Rahul Tyagi
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Multibranch Loops (MBL)
http://www.stanford.edu/~esorin
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A step towards tertiary structure prediction
Secondary structure representation
1 stacked on 2 mediated by mismatch
2 flush stacked on 3
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Flush and Mismatch-Mediated Stacking
Mismatch-mediated stacking
Flush stacking
- Stacking stabilization: Thought to arise from hydrophobic effect, charge interactions and van der Waals interactions.
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Predicting Coaxial Stacking
- Find all the non-redundant RNA crystal structures from NDb.
“The stacking configuration with lowest free energy as predicted by Nearest Neighbour Parameters exists in naturally occurring RNAs.”
- Compare predictions with crystal structures.
- Predict the coaxial stacking configuration by finding free energy of all possible configurations in all MBLs.
Hypothesis
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Finding Lowest Free Energy Configuration
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Secondary structure to predicted stacks
http://www.rna.icmb.utexas.edu/
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Nearest Neighbor Model for Coaxial Stacking
Model based on work by Walter, Kim and others in Turner lab.
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Stacks with more than one Mismatch
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Identifying Coaxial Stacks in Crystal Structures
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Atom Coordinates to Identified Stacks
http://rna.ucsc.edu/rnacenter/ribosome_images.html
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Stacking Definition for Verification
Basepair center and basepair plane definition
from Biochemistry 2nd Ed. by Garrett & Grisham
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Coaxial Stacking Discovery
Criteria for stacking
a. Basepair plane tilt< 26º for Flush / 32º for MM
N1
N1N2
D1-2
b. Distance between basepair “centers” < 5 Å for Flush / 12 Å for MM
(based on Gabb et al., J. Mol. Graph., 14, 6-11Burkard et al., JMB, 290, 967-982and Gendron at al., JMB, 308, 919-936
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Stacking Definition for Verification
c. Basepair shear
angle between inter-center vector
and baseplane normal vectors
< 60º
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Capturing Complex Stacks
relaxed tilt and distance criteria:
distance of basepair centers from normal to the other basepair < 10 Å
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Capturing Complex Stacks
Base Stack Cascade
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Results : Comparison of Predictions with Reality
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RNA structure dataset
The ribosome RNA structures provide maximum data.
Data distribution by RNA type
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tRNA ribozymes rRNA others
RNA type
nu
mb
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MB
Ls/
stack
s
MBLs Predicted Stacks Total Stacks
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Results
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Dependence on MBL Size(no. of branches)
PPV and Sensitivity dependence on number of branches in MBLs
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3 4 5 6 7 8
Number of branches
PP
V/S
en
sitiv
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(%
)
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nu
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PPV Sensitivity MBLs
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Dependence on MBL Size(no. of bases)
PPV and sensitivity dependence on the size of MBL
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8-11 12-15 16-19 20-23 24-27 28-31 32-35 36-39 40-56
number of bases in MBL
PP
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sitiv
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(%
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nu
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PPV Sensitivity number of MBLs
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A four way MBL:
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Expanding to a partition function:
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Suboptimal ConfigurationsThe Problem with Lowest Free Energy
Consider,
K3/2 < K1, K2 < K3
A stack is more probable if it is part of many different configurations of low free energy.
Just 4 out of 51 possible configurations!
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Partition Function and Configuration Probabilities
• PT = Σi exp(-ΔGi/RT) where i varies over ALL the possible configurations.
• PR,S = Σj exp(-ΔGj/RT) where j varies over all the possible configurations that have stack S.
• ps = PR,S / PT
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Probability Threshold for Prediction
Both plots show a sharp drop at 0.70
So 70% was chosen to be the cut-off value for prediction
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Partition Function Results
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Conclusion:
• Predicting coaxial stacking by free energy minimization provides a method to predict the topology of tertiary structure.