RNA secondary structure prediction and runtime optimization Greg Goldgof October 5, 2006 CS374 Presentation Stanford University

Presentation Overview  Background on RNA secondary structure prediction  CONTRAfold: probabilistic RNA folding  How is RNA folding done from an algorithmic perspective?  Other RNA folding methods: Physics-based methods and SCFGs  CandidateFold: RNA folding in O(n 2 )  Genome-wide accessible motif detection

What are RNA and mRNA?  Traditional role as messenger molecule (mRNA)  RNA is a polymer of nucleotides A, U, C, and G transcribed from DNA GATTACA GAUUACA

What is RNA secondary structure/folding? bulge loop helix (stem) hairpin loop internal loop multi-branch loop

Pseudoknots  Pseudoknots will not be treated in this talk.  Not dealt with by either paper.

non-coding RNA (RNA genes)  RNA enzymes: catalytic RNA  Ribosomal RNA (rRNA)  Transfer RNA (tRNA)  RNAi: RNA mediated gene regulation  Micro RNA (miRNA)  Short-interfering RNA (siRNA)  Alternative splicing: small-nuclear RNA (snRNA)  Others: snoRNA, eRNA, srpRNA, tmRNA, gRNA Structure essential to function for many ncRNAs

Presentation Overview  Background on RNA secondary structure prediction  CONTRAfold: probabilistic RNA folding  How is RNA folding done from an algorithmic perspective?  Other RNA folding methods: Physics-based methods and SCFGs  CandidateFold: RNA folding in O(n 2 )  Genome-wide accessible motif detection

CONTRAfold Problem: Given an RNA sequence, predict the most likely secondary structure AUCCCCGUAUCGAUC AAAAUCCAUGGGUAC CCUAGUGAAAGUGUA UAUACGUGCUCUGAU UCUUUACUGAGGAGU CAGUGAACGAACUGA

How does CONTRAfold work?  CONTRAfold looks at features that indicate a good structure  C-G base pairings  A-U base pairings  Helices of length 5  Hairpin loops of size 9  Bulge loops of size 2  CG/GC Base-pair stacking interactions For example:  These examples are called thermodynamic parameters because they represent free energy values

How does CONTRAfold choose a structure?  Every feature f i is associated with a weight w i.  The probability of a structure y, given a sequence x, is determined by the following relationship: ) ( exp structuresequence weight of Feature i # of occurrences of feature i, in structure y generated from sequence x

How does CONTRAfold choose a structure? Cont’d  Considers all structures and finds optimal structure via dynamic programming in O(n 3 )  Added bonus: probability associated with each base Low confidence bases lighter High confidence bases darker

Parameter γ allows trade-off between sensitivity and specificity Sensitivity = # correct base pairings # true base pairings Specificity = # correct base pairings # predicted base pairings  = 1  = 8  = 1024 AUCCCCGUAUCGAUC AAAAUCCAUGGGUAC CCUAGUGAAAGUGUA UAUACGUGCUCUGAU UCUUUACUGAGGAGU CAGUGAACGAACUGA

CONTRAfold learns how to predict good structures  CONTRAfold trains on set of published examples of known RNA structures taken from a database called Rfam (RNA families)  CONTRAfold learns the relative value, or weight, of each of its features  CONTRAfold determines the weight for each feature that maximizes its performance on the training set.  A training set is a collection of known correct solutions that a program learns from.

CONTRAfold Performance

Presentation Overview  Background on RNA secondary structure prediction  CONTRAfold: probabilistic RNA folding  How is RNA folding done from an algorithmic perspective?  Other RNA folding methods: Physics-based methods and SCFGs  CandidateFold: RNA folding in O(n 2 )  Genome-wide accessible motif detection

Other Methods Stochastic context-free grammars Physics-based models

 All features reflect thermodynamic interactions  Features experimentally determined in lab, rather than learned Disadvantages to CONTRAfold  Thermodynamic weights difficult to calculate  No incorporation of non-thermodynamic features  Cannot be tailored to specific families of RNAs since weights always the same  Cannot trade off between sensitivity and specificity  No associated probabilities with each pair-bonding  Until CONTRAfold, best performing method

acuSag Stochastic context-free grammars  Based on grammar rules with associated probabilities S  aSu | cSg | aS | uS | … | Su | SS | ε P S aSaS acSgacSg acuSuag acugScuag acuguScuag acuguaScuag acuguauScuag acuguaucuag.(((...).))  Let’s generate a structure for the sequence acuuauuag acuguacuag.(((..).)) acugucuag.(((.).)) acugcuag.((().)) acuuag.((.)) acuag.(()) acg.() a.a.  We select the set of transformations that highest probability of generating the input sequence. This set gives us our structure.

Stochastic context-free grammars cont’d Disadvantages to CONTRAfold  Grammar rules of SCFG less expressive than features of CONTRAfold or physics-based methods  Poor accuracy: always dominated by physics-based models  Like CONTRAfold, transformation probabilities can be automatically trained  Therefore, they can also be optimized to specific datasets  Provide an associated probability with a given structure

Advantages of CONTRAfold  High accuracy  Automated training of parameters  Can be tuned to specific data  Provides associated probabilities for each base-pairing  Ability to control sensitivity/specificity trade-off  Can incorporate both physics-based and non-thermodynamic parameters

Presentation Overview  Background on RNA secondary structure prediction  CONTRAfold: probabilistic RNA folding  How is RNA folding done from an algorithmic perspective?  Other RNA folding methods: Physics-based methods and SCFGs  CandidateFold: RNA folding in O(n 2 )  Genome-wide accessible motif detection

How is RNA folding done? Simple Nussinov Folding Algorithm  Only scores interactions between paired bases  Useful for demonstrating general structure of more complex folding algorithms Score for optimal structure from base i to base j Base i is unpaired, consider pairing between i+1 and j We want the highest scoring fold Base j is unpaired, consider pairing between i and j-1 δ (i, j) = score for a pairing between i and j.

How is RNA folding done? Simple Nussinov Folding Algorithm  Only scores interactions between paired bases  Useful for demonstrating general structure of more complex folding algorithms Pair i and j. Now consider pairing between i+1 and j-1.

How is RNA folding done? Simple Nussinov Folding Algorithm  Only scores interactions between paired bases  Useful for demonstrating general structure of more complex folding algorithms i and j begin a bifurcation. Consider every possible bifurcation point k. Sum scores from each folded structure.

How is RNA folding done?  What is the runtime of the Nussinov algorithm?  All possible value of iO(n)  All possible values of j O(n) For a given sequence of length n = j – i we must consider: For each i we must consider: For each i, j pair we must consider:  All possible values of k O(n) O(n) * O(n) * O(n) → O(n 3 )

A more sophisticated algorithm  We want to take into account more advanced features than just base-pairings.

i j What is V(i, j)? eh = Energy of a hairpin closed at i and j

What is V(i, j)? es = Energy of stacked pair i, j and i+1, j-1 i j

What is V(i, j)? ebi = Energy of a bulge or interior loop that begins at i, j and is closed at i ’, j ’ i j i’i’ j’j’

What is V(i, j)? Same old bifurcation equation, but i is paired to j

What is its runtime?  Still only O(n 3 ) because we are only recursing on i, j, and k  This equation theoretically O(n), however, it is standard to bound RNA interior loops by a constant (30), making it O(1)

Presentation Overview  Background on RNA secondary structure prediction  CONTRAfold: probabilistic RNA folding  How is RNA folding done from an algorithmic perspective?  Other RNA folding methods: Physics-based methods and SCFGs  CandidateFold: RNA folding in O(n 2 )  Genome-wide accessible motif detection

CandidateFold  Same folding as complex model in O(n 2 ψ(n)), where ψ(n) is shown to a constant  What does it do?  Imposes some constraints on W and V  How does it do it? From WFrom V  Rather than trying all k, they keep a list of candidate positions reducing this step to O(1) time

CandidateFold  Much faster RNA folding  What is the advantage of CandidateFold?  Accessible motif finding  What is an application of high-speed RNA folding?

Presentation Overview  Background on RNA secondary structure prediction  CONTRAfold: probabilistic RNA folding  How is RNA folding done from an algorithmic perspective?  Other RNA folding methods: Physics-based methods and SCFGs  CandidateFold: RNA folding in O(n 2 )  Genome-wide accessible motif detection

What is an RNA regulatory motif?  Motif: A conserved sequence element  A regulator binds to a regulatory motif  RNA regulatory motif: A motif used to regulate translation G A U U A C A... RNA Regulatory motif (AUUAC)  Regulatory protein  Micro RNA U A A U G microRNA

What is an accessible motif?  If a sequence is part of an intramolecular hybridization, it is unlikely to bind to regulators  We define a motif as “accessible” if none of its nucleotides is hybridized as part of the folding

Accessible motifs cont’d  Therefore, only accessible sequences should be scanned for regulatory motifs

Accessible motifs cont’d  Therefore, only accessible sequences should be scanned for regulatory motifs.

How do Wexler et al. detect regulatory motifs?  Stage 1: Process sequence set G to extract all “accessible windows”  Run sliding window of size k across each mRNA sequence  Find the minimal energy fold for the sequence, assuming none of the bases in the window are paired  If the energy of this folding minus the energy of a normal folding of the mRNA < δ, then accept the window Problem: Given a set of mRNAs G, a parameter k denoting motif window size, and a pre-defined energy threshold δ, find the regulatory motifs  Stage 2: Search for regulatory motifs among the “accessible windows”  Motif finding will be discussed in later lectures

Results: Degradation Related Motifs

Results: Tissue Specific microRNAs Silique: A long, slender, many-seeded, cylindrical fruit of the Mustard Family

The End

Works Cited CB Do, DA Woods, S Batzoglou. CONTRAfold: RNA secondary structure prediction without physics-based models. Bioinformatics, 22(14): e90-e98, Y Wexler, C Zilberstein, M Ziv-Ukelson. A Study of Accessible Motifs and RNA Folding Complexity. Recomb 2006, LNBI 3909: , 2006.