Predicting Coaxial Stacking by Free Energy Minimization

1
Predicting Coaxial Stacking by Free Energy
Minimization

• David Mathews
• Department of Biochemistry Biophysics
• University of Rochester Medical Center

2
Predicting Coaxial Stacking

• Rahul Tyagi

3
Multibranch Loops (MBL)
http//www.stanford.edu/esorin
4
A step towards tertiary structure prediction
1 stacked on 2 mediated by mismatch
Secondary structure representation
2 flush stacked on 3
5
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.

6
Predicting Coaxial Stacking
Hypothesis
The stacking configuration with lowest free
energy as predicted by Nearest Neighbour
Parameters exists in naturally occurring RNAs.

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

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

• Compare predictions with crystal structures.

7
Finding Lowest Free Energy Configuration
8
Secondary structure to predicted stacks
http//www.rna.icmb.utexas.edu/
9
Nearest Neighbor Model for Coaxial Stacking
Model based on work by Walter, Kim and others in
Turner lab.
10
Stacks with more than one Mismatch
11
Identifying Coaxial Stacks in Crystal Structures
12
Atom Coordinates to Identified Stacks
http//rna.ucsc.edu/rnacenter/ribosome_images.html
13
Stacking Definition for Verification
Basepair center and basepair plane definition
from Biochemistry 2nd Ed. by Garrett Grisham
14
Coaxial Stacking Discovery

• Criteria for stacking
• a. Basepair plane tilt
• lt 26º for Flush / 32º for MM

N1
N2
N1
b. Distance between basepair centers lt
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
15
Stacking Definition for Verification
c. Basepair shear angle between
inter-center vector and baseplane normal
vectors lt 60º
16
Capturing Complex Stacks
relaxed tilt and distance criteria distance
of basepair centers from normal to the other
basepair lt 10 Å
17
Capturing Complex Stacks
Base Stack Cascade
18
Results Comparison of Predictions
with Reality
19
RNA structure dataset
The ribosome RNA structures provide maximum data.
20
Results
21
Dependence on MBL Size(no. of branches)
22
Dependence on MBL Size(no. of bases)
23
A four way MBL
24
Expanding to a partition function
25
Suboptimal ConfigurationsThe Problem with Lowest
Free Energy
Just 4 out of 51 possible configurations!
Consider, K3/2 lt K1, K2 lt K3
A stack is more probable if it is part of many
different configurations of low free energy.
26
Partition Function and Configuration Probabilities

• PT Si exp(-?Gi/RT) where i varies over ALL the
  possible configurations.
• PR,S Sj exp(-?Gj/RT) where j varies over all
  the possible configurations that have stack S.
• ps PR,S / PT

27
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
28
Partition Function Results
29
Conclusion

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