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Improved RNA Secondary Structure Prediction by Maximizing Expected Pair Accuracy. Zhi John Lu, Jason Gloor, and David H. Mathews University of Rochester Medical Center, Rochester, New York. RNA Secondary and Tertiary Structure:. AAUUGCGGGAAAGGGGUCAA CAGCCGUUCAGUACCAAGUC

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Improved RNA

Secondary Structure Prediction by Maximizing

Expected Pair Accuracy

Zhi John Lu, Jason Gloor, and David H. MathewsUniversity of Rochester Medical Center, Rochester, New York

RNA Secondary and Tertiary Structure:









Cate, et al. (Cech & Doudna).

(1996) Science 273:1678.

Waring & Davies. (1984) Gene 28: 277.

Gibbs Free Energy Change:

Ki =


= Ki/Kj =

The structure with the lowest DG° is the

most favored at a given temperature.

Nearest Neighbor Model for Free Energy Change of a Sample Hairpin Loop:

Mathews et al., J. Mol. Biol., 1999, 288: 911.

Mathews et al., PNAS, 2004, 101: 7287.

Rna secondary structure prediction accuracy
RNA Secondary Structure Prediction Accuracy: Hairpin Loop:

Percentage of Known Base Pairs Correctly Predicted:

Mathews, Disney, Childs, Schroeder, Zuker, & Turner. 2004. PNAS 101: 7287.

Limitations to prediction of the minimum free energy structure
Limitations to Prediction of the Minimum Free Energy Structure:

  • A minimum free energy structure provides the single best guess for the secondary structure.

  • Assumes that:

    • RNA is at equilibrium

    • RNA has a single conformation

    • RNA thermodynamic parameters are without error

      • Non-nearest neighbor effects

      • Some sequence-specific stabilities are averaged

A method that looks at the probability of a structure could be more informative
A Method that Looks at the Probability of a Structure could be more Informative:

  • A partition function can be used to determine the probability of a structure at equilibrium.

The partition function q
The Partition Function, Q: be more Informative:

So what is q good for
So, what is Q good for? be more Informative:

where k is the sum over all structures with the i-j base pair.

Accuracy: be more Informative:

  • Sensitivity – what percentage of known pairs occur in the predicted structure.

  • Positive Predictive Value (PPV) – what percentage of predicted pairs occur in the known structure.

  • PPV ≤ Sensitivity because the structures determined by comparative sequence analysis do not have all pairs and there is a tendency to over-predict base pairs by free energy minimization.

Applying p i j to structure prediction
Applying P be more Informative:i,j to Structure Prediction:


PBP≥ 90%


PBP≥ 70%


PBP> 50%



Value (PPV)


PBP≥ 99%


PBP≥ 95%


Mathews. RNA. 10: 1178. (2004).

Percent of predicted bp above threshold
Percent of Predicted BP above Threshold: be more Informative:


PBP≥ 99%


PBP≥ 95%


PBP≥ 90%


PBP≥ 70%


PBP> 50%

Mathews. RNA. 10: 1178. (2004).

Color annotation
Color Annotation: be more Informative:

E. coli 5S rRNA

Structures constructed from highly probable pairs
Structures Constructed from Highly Probable Pairs: be more Informative:

PBP≥ 99%

PBP≥ 90%

PBP≥ 70%

PBP> 50%

CONTRAfold: be more Informative:

  • “Statistical learning method” to predict Pi,j

  • Generate structures:


Bioinformatics. 22: e90-e98. (2006).

Implement maximum expectation
Implement Maximum Expectation: be more Informative:

  • Zhi John Lu, Jason Gloor, David Mathews

  • Implement dynamic programming algorithm

    using partition function prediction of Pi,j.

  • Also implement suboptimal structure prediction.

    • Alternative hypotheses.

Sensitivity and ppv vs g
Sensitivity and PPV vs. be more Informative:g:

Comparison: be more Informative:

Summary: be more Informative:

  • Maximizing expected accuracy can predict structures with greater sensitivity and positive predictive value than free energy minimization.

  • Maximizing expected accuracy using an underlying thermodynamic model is more accurate than an underlying statistical model.

Methanococcus thermolithotrophicus be more Informative: 5S rRNA (Szymanski et al., 1998):

MaxExpect Predicted Structure:

Minimum Free Energy Structure: be more Informative:


Predicted Structure: