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

Secondary structure representation

1 stacked on 2 mediated by mismatch

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.

“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

Finding Lowest Free Energy Configuration

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.

Stacks with more than one Mismatch

Identifying Coaxial Stacks in Crystal Structures

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

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

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.

Data distribution by RNA type

0

10

20

30

40

50

60

70

80

90

100

tRNA ribozymes rRNA others

RNA type

nu

mb

er

of

MB

Ls/

stack

s

MBLs Predicted Stacks Total Stacks

Results

Dependence on MBL Size(no. of branches)

PPV and Sensitivity dependence on number of branches in MBLs

0

10

20

30

40

50

60

70

80

90

100

3 4 5 6 7 8

Number of branches

PP

V/S

en

sitiv

ity

(%

)

0

20

40

60

80

100

120

nu

mb

er o

f MB

Ls

PPV Sensitivity MBLs

Dependence on MBL Size(no. of bases)

PPV and sensitivity dependence on the size of MBL

0

10

20

30

40

50

60

70

80

90

100

8-11 12-15 16-19 20-23 24-27 28-31 32-35 36-39 40-56

number of bases in MBL

PP

V/S

en

sitiv

ity

(%

)

0

5

10

15

20

25

30

35

40

45

50

nu

mb

er o

f MB

Ls

PPV Sensitivity number of MBLs

A four way MBL:

Expanding to a partition function:

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!

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

Partition Function Results

Conclusion:

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