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The Discovery of Novel ncRNA in Genomes. Andrew Uzilov David Mathews. Uzilov, Keegan, Mathews. BMC Bioinformatics . 2006. In Press. Outline:. Background in ncRNA. Basic hypothesis. The Dynalign algorithm for prediction of an RNA secondary structure common to two sequences.

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the discovery of novel ncrna in genomes

The Discovery of Novel ncRNA in Genomes

Andrew Uzilov

David Mathews

  • Background in ncRNA.
  • Basic hypothesis.
  • The Dynalign algorithm for prediction of an RNA secondary structure common to two sequences.
  • Using Dynalign to find ncRNA sequences in genomes.
  • Optimizing Dynalign performance.

What is ncRNA?

  • Non-coding RNA (ncRNA) is an RNA that functions without being translated to a protein.
  • Known roles for ncRNAs:
    • RNA catalyzes excision/ligation in introns.
    • RNA catalyzes the maturation of tRNA.
    • RNA catalyzes peptide bond formation.
    • RNA is a required subunit in telomerase.
    • RNA plays roles in immunity and development (RNAi).
    • RNA plays a role in dosage compensation.
    • RNA plays a role in carbon storage.
    • RNA is a major subunit in the SRP, which is important in protein trafficking.
    • RNA guides RNA modification.

Predicting RNA Secondary and 3D Structure from Sequence:









Cate, et al. (Cech & Doudna).

(1996) Science 273:1678.

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


An RNA Secondary Structure:

R2 Retrotransposon

3’ UTR from D. melanogaster.

RNA 3:1-16.

On average, 46 % of

nucleotides are unpaired.


Gibb’s Free Energy (DG°):

Ki =


= Ki/Kj =

DG° quantifies the favorability of a structure

at a given temperature.


Nearest Neighbor Model for RNA Secondary Structure Free Energy at 37 OC:

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

how is the lowest free energy structure determined
How is the Lowest Free Energy Structure Determined?
  • Naïve approach would be to calculate the free energy of every possible secondary structure.
  • Number of secondary structures  1.8N (where N is the number of nucleotides)
  • The free energies of 1000 structures can be calculated in 1 second.
  • For 100 nucleotide sequence:
    • Number of secondary structures  3 × 1025
    • Time to calculate  1014 years
dynamic programming algorithm
Dynamic Programming Algorithm:
  • Not to be confused with molecular dynamics.
  • This is a calculation – not a simulation.
  • The lowest free energy structure is guaranteed given the nearest neighbor parameters used.
  • Reviewed by Sean Eddy. Nature Biotechnology. 2004. 11: 1457.
dynamic programming algorithm13
Dynamic Programming Algorithm:
  • Named by Richard Bellman in 1953.
  • Applies to calculations in which the cost/score is built progressively from smaller solutions.
  • Other applications
    • Sequence alignment
    • Determining partition functions for RNA secondary structures
    • Finding shortest paths
    • Determining moves in games
    • Linguistics
dynamic programming
Dynamic Programming:
  • Recursion is used to speed the calculation.
    • The problem is divided into smaller problems.
    • The smaller problems are used to solve bigger problems.
  • Two Step Process
    • Fill – determines the lowest free energy folding possible for each subsequence
    • Traceback – determined the structure that has the lowest free energy
rna secondary structure prediction accuracy
RNA Secondary Structure Prediction Accuracy:

Percentage of Known Base Pairs Correctly Predicted:

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


i < i’ < j < j’

  • ncRNAs have lower folding free energy change than non-structural sequences, e.g. mRNA, or random sequences.
  • Corollary:
    • ncRNAs, which are structured, can be found in genomic sequences because they have folding free energy change lower than background sequences.
do structural rnas have lower folding free energy change than background
Do Structural RNAs have Lower Folding Free Energy Change than Background?
  • Yes:
    • Le et al. 1990. NAR 18:1613.
    • Seffens & Digby. 1999. NAR 27:1578.
    • Clote et al. 2005. RNA 11:578.
  • No:
    • Workman & Krogh. 1999. NAR 27:418.
    • Rivas & Eddy. 2000. Bioinformatics 16:583.
test of hypothesis
Test of Hypothesis:


(tRNA or 5S rRNA)


(First order Markov

chain that preserves

dinucleotide frequencies)

(First order Markov chain

that preserves

dinucleotide frequencies)

100 Control


100 Control


calculate z score of folding free energy change for positives and negatives
Calculate Z Score of Folding Free Energy Change for Positives and Negatives:
  • Calculate the mean, <DG37>, and standard deviation, s, for the controls.
  • Z score is the number of standard deviations that a negative or positive’s free energy change is different from mean:

Z = (DG37-<DG37>)/ s

  • Choose a Z-score cutoff for classification as ncRNA.
  • Sensitivity =

(True Positives)/(True Positives + False Negatives) =

percent of ncRNA correctly classified as ncRNA

  • Specificity =

(True Negatives)/(True Negatives + False Positives) =

percent of non-ncRNA correctly classified as non-ncRNA

why do structural rna sequences not have a significantly lower folding free energy change
Why do Structural RNA Sequences Not Have a Significantly Lower Folding Free Energy Change?
  • Hypothesis is incorrect.
  • Secondary structure prediction has limited accuracy:
    • Kinetics may play a role in folding.
    • Free energy nearest neighbors are based on a limited number of experiments and have error.
    • The algorithms that are used for these studies cannot predict pseudoknots (non-nested pairs).

Dynalign (a 4-D Dynamic Programming Algorithm):

Algorithm for

Secondary Structure Prediction

(2D dynamic programming algorithm)

Algorithm for

Sequence Alignment

(2D dynamic programming algorithm)

Simultaneously finds the sequence alignment and

thermodynamically favorable common secondary structure

for two sequences.

Dynalign requires no sequence identity.

Mathews & Turner. Journal of Molecular Biology. 317: 191-203 (2002)

Mathews. Bioinformatics. 21: 2246-2253 (2005)


Inputs, Optimization, and Outputs:


Sequence 1

Sequence 2

Optimization (minimize DG°total):

DG°total = DG°sequence 1 + DG°sequence 2 + (DG°gap)(number of gaps)


Sequence Alignment, Structure of 1, Structure of 2

where each helix in 1 must be homologous to a BP in 2


Optimization of DGºgap:

Seven 5S rRNAs with secondary structures predicted with 47.8% average

accuracy. Average of all 42 pair-wise combinations predicted by Dynalign.


Improving the Accuracy of tRNA

Secondary Structure Prediction:

Conventional Free Energy Minimization Predicted Structures:




Improving the Accuracy of tRNA

Secondary Structure Prediction:

Dynalign Predicted Structures:





^^^^^^^ ^^^^ ^^^^ ^^^^^ ^^^^^ ^^^^^ ^^^^^^^^^^^^

  • Four databases:
    • All pairwise comparisons (21) of seven 5S sequences with widely varying accuracy of secondary structure prediction using a single sequence.
    • 3 calculations with 6 srp sequences.
    • All pairwise calculations (780) with 40 randomly chosen tRNA sequences.
    • All pairwise comparisons (105) of 15 randomly chosen 5S rRNA sequences.

Sensitivity = (Correctly Predicted Pairs)/(Total Known Pairs)

improving dynalign performance
Improving Dynalign Performance:
  • The original restriction on the alignments is: |i – k| ≤ M
    • For the 3’ ends of the sequence to align: M ≥ | N1 – N2|
    • For most applications, the ends of the sequences should align.
  • This suggests an alternative restriction: |i N2/N1 – k | ≤ M
    • This allows a smaller M parameter. Calculation time scales O(N3M3).
heuristic to exclude base pairs
Heuristic to Exclude Base Pairs:
  • There are many possible canonical base pairs that are not worth considering because any structure that contains them has a high free energy.
  • The “high energy” base pairs can be identified by secondary structure prediction using a single sequence (very fast). The high energy pairs can then be excluded from a Dynalign structure prediction.
of known pairs within a energy increment from the lowest free energy structure
% of Known Pairs within a % Energy Increment from the Lowest Free Energy Structure:
time performance improvement
Time Performance Improvement:

3.2 GHz Intel Pentium 4 with 1 GB RAM; Red Hat Enterprise Linux 3;

gcc 3.2.3-42 compiler

revised hypothesis
Revised Hypothesis:
  • Dynalign calculated folding free energies for sequence pairs derived from genome alignments can be used to find ncRNAs with high sensitivity and specificity.
testing the hypothesis
Testing the Hypothesis:

ncRNA pair

(tRNAs or 5S rRNAs)

Negative pair

(Shuffle of global alignment)

(Shuffle of global alignment)

20 Control

Sequence Pairs

20 Control

Sequence Pairs

comparison to other state of the art methods
Comparison to Other State of the Art Methods:
  • QRNA:
    • Rivas & Eddy. 2001. BMC Bioinformatics 2:8.
    • Comparative analysis of aligned sequences, where compensating base pairs changes indicate ncRNA. Classification by stochastic context-free grammar.
  • RNAz:
    • Washietl, Hofacker, & Stadler. 2005. PNAS 102: 2454.
    • Folding free energy of two or more aligned sequences using RNAalifold. Classification by support vector machine (SVM).
  • Both Methods Use Fixed Alignments:
    • Faster than Dynalign.
    • Limited to sequence alignment algorithm (compensating base pair changes make accurate alignment difficult).
human vs mouse alignment santa cruz genome server pairwise identities for 50 nucleotide windows
Human vs. Mouse Alignment (Santa Cruz Genome Server) Pairwise Identities for 50 Nucleotide Windows:
faster method using dynalign
Faster Method Using Dynalign:
  • Run a single calculation and use a support vector machine (SVM) to classify sequence as ncRNA or not.
    • Each window only needs to be scanned once.
    • A probability is assigned to the classification.
  • SVM
    • Trained with tRNA and 5S rRNA sequences.
    • Input:
      • Dynalign total free energy change
      • Length of the shorter sequence
      • A,C,G content of each sequence
unrolling the method on e coli
Unrolling the Method on E. coli:
  • Look for ncRNA in E. coli using alignments to S. typhi.
    • MUMmer (Kurtz et al.. 2004. Genome Biol 5:R12)
      • 15,214 blocks of 50 to 150 nucleotides as above (where long alignment blocks were divided into 150 nucleotide windows that overlap 75 nucleotides)
epilogue improving dynalign performance
Epilogue: Improving Dynalign Performance:
  • In collaboration with Gaurav Sharma, Electrical and Computer Engineering, University of Rochester, and Arif Harmanci, we pre-determine the sequence alignment probabilities with a Hidden Markov Model.
  • Then, we only allow alignments in Dynalign that have probability greater than 10-4.
    • This removes the need of using the M parameter heuristic.
    • This does not affect the accuracy of structure prediction by Dynalign.
benchmarks against other programs using 2000 pairs of 5s rrna sequences
Benchmarks Against Other Programs Using 2000 Pairs of 5S rRNA Sequences:

Percent of Known Pairs Correctly Predicted:

performance benchmarks using 200 pairs of sequences
Performance Benchmarks Using 200 Pairs of Sequences:

Using a single core on a dual, dual-core Opteron 270 machine

running Fedora Core 5 and gcc 4.1.1.

parallelizing dynalign for smp
Parallelizing Dynalign for SMP:
  • In collaboration with Paul Tymann, Computer Science, Rochester Institute of Technology and CS students Chris Connett, Glenn Katzen, Andrew Yohn, we developed an SMP version of Dynalign.
  • This takes advantage of the fact that there are a number of positions in the arrays that can be filled independently in the dynamic programming algorithm recursions.

Two R2 3’ UTRs of length 234 and 217 nucleotides.

Using a dual, dual-core Opteron 270 machine running Fedora Core 5 and gcc 4.1.1.

preliminary results with smp dynalign
Preliminary Results with SMP-Dynalign:
  • Single sequence secondary structure prediction of E. coli 16S rRNA (1542 nucleotides) has 43.6% sensitivity.
  • E. coli 16S rRNA run on Dynalign with:
    • B. subtilis 16S rRNA (1552 nucleotides) has 80.7% sensitivity and required 381 minutes on 4 cores and 983 MB or RAM.
    • Borrelia burgodorferi 16S rRNA (1532 nucleotides) has 76.4% sensitivity and required 408 minutes on 4 cores and 1.0 GB of RAM.
  • The folding free energy of single sequences does not provide a sensitive and specific method of finding ncRNAs. It does, however, provide a pre-filtering method that can remove 30% of sequences from consideration.
  • Dynalign shows promise as a method for ncRNA detection, especially at low pairwise identities of sequences.
  • Funding:
    • Alfred P. Sloan Foundation
    • National Institutes of Health
  • Computing:
    • CASCI Lab at Rochester Institute of Technology
  • Past Lab Members:
    • Andrew Uzilov
    • Shan Zhao
    • Eliany Sanchez-Baez
  • Lab Members:
    • Sumeet Chandha
    • Zhi Lu
    • Matthew Seetin
    • Rahul Tyagi
    • Keith VanNostrand