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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.
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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.