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Predicting Coaxial Stacking by Free Energy MinimizationPowerPoint Presentation

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

Results : Comparison of Predictions with Reality

RNA structure dataset

The ribosome RNA structures provide maximum data.

Dependence on MBL Size(no. of branches)

Dependence on MBL Size(no. of bases)

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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