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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

Predicting Coaxial Stacking:

- Rahul Tyagi

Multibranch Loops (MBL)

http://www.stanford.edu/~esorin

A step towards tertiary structure prediction

1 stacked on 2 mediated by mismatch

Secondary structure representation

2 flush stacked on 3

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.

Predicting Coaxial Stacking

- Find all the non-redundant RNA crystal structures from NDb.

Hypothesis

“The stacking configuration with lowest free energy as predicted by

Nearest Neighbour Parameters exists in naturally occurring RNAs.”

- Predict the coaxial stacking configuration by finding free energy of all possible configurations in all MBLs.

- Compare predictions with crystal structures.

Secondary structure to predicted stacks

http://www.rna.icmb.utexas.edu/

Nearest Neighbor Model for Coaxial Stacking

Model based on work by Walter, Kim and others in Turner lab.

Atom Coordinates to Identified Stacks

http://rna.ucsc.edu/rnacenter/ribosome_images.html

Stacking Definition for Verification

Basepair center and basepair plane definition

from Biochemistry 2nd Ed. by Garrett & Grisham

Coaxial Stacking Discovery

N1

Criteria for stacking

a. Basepair plane tilt

< 26º for Flush / 32º for MM

N2

N1

b. Distance between basepair “centers”

< 5 Å for Flush / 12 Å for MM

(based on Gabb et al., J. Mol. Graph., 14, 6-11

Burkard et al., JMB, 290, 967-982

and Gendron at al., JMB, 308, 919-936

D1-2

Stacking Definition for Verification

c. Basepair shear

angle between inter-center vector

and baseplane normal vectors

< 60º

Capturing Complex Stacks

relaxed tilt and distance criteria:

distance of basepair centers from normal to the other basepair < 10 Å

Capturing Complex Stacks

Base Stack Cascade

RNA structure dataset

The ribosome RNA structures provide maximum data.

Suboptimal ConfigurationsThe Problem with Lowest Free Energy

Just 4 out of 51 possible configurations!

Consider,

K3/2 < K1, K2 < K3

A stack is more probable if it is part of many different configurations of low free energy.

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

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

Conclusion:

- Predicting coaxial stacking by free energy minimization provides a method to predict the topology of tertiary structure.

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