Lecture7:RNAfolding

Chapter6–Problem6.51inJonesandPevznerandtheTurnermodel

Fall2019

September19,2019

RNABasics

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�  RNAbasesA,C,G,U�  CanonicalBasePairs◦  A-U◦  G-C◦  G-U“wobble”pairing◦  Basescanonlypairwithoneotherbase.

Image: http://www.bioalgorithms.info/

RNAStructuralLevels

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Primary AAUCG...CUUCUUCCA Primary

Secondary Tertiary

RNASecondaryStructure

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Hairpin loop Junction (Multiloop)

Bulge Loop

Single-Stranded

Internal Loop

Stack

Pseudoknot

BasePairMaximization

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U

C

C

A G

G

A

C

Zuker (1981) Nucleic Acids Research 9(1) 133-149

BasePairMaximization–DynamicProgrammingAlgorithm

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Simple Example: Maximizing Base Pairing

BasePairMaximization–DynamicProgrammingAlgorithm

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S(i,j) is the folding of the subsequence of the RNA strand from index i to index j which results in the highest number of base pairs

BasePairMaximization–DynamicProgrammingAlgorithm

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BasePairMaximization–DynamicProgrammingAlgorithm

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BasePairMaximization–DynamicProgrammingAlgorithm

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BasePairMaximization–DynamicProgrammingAlgorithm

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CircularRepresentation

12 Images – David Mount

Pseudoknots

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�  PseudoknotscauseabreakdowninthepresentedDynamicProgrammingAlgorithm.

�  Inordertoformapseudoknot,checksmustbemadetoensurebaseisnotalreadypaired–thisbreaksdownthedivideandconquerrecurrencerelations.

Images – David Mount

SimplifyingAssumptions

•  RNAfoldsintooneminimumfree-energystructure.

•  Therearenoknots(basepairsnevercross).•  Theenergyofaparticularbasepairinadoublestrandedregionissequenceindependent.•  Neighborsdonotinfluencetheenergy.

• Wassolvedbydynamicprogramming,ZuckerandSteigler1981

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SequenceDependentBasePairEnergyValues(NearestNeighborModel)

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U U C G G C A U G C A UCGAC 3’ 5’

U U C G U A A U G C A UCGAC 3’

5’

Example values: GC GC GC GC AU GC CG UA -2.3 -2.9 -3.4 -2.1

FreeEnergyComputation(NearestNeighborModel)

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U U A A G C G C A G C U A A U C G A U A 3’ A 5’

-0.3

-0.3

-1.1 mismatch of hairpin -2.9 stacking

+3.3 1nt bulge -2.9 stacking

-1.8 stacking

5’ dangling

-0.9 stacking -1.8 stacking -2.1 stacking

G= - 4.9 kcal/mol

+5.9 4 nt loop

RNASecondaryStructure

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Stack

NearestNeighborModel

•  Stackingenergy-assignnegativeenergiestothesebetweenbasepairregions.•  Energyisinfluencedbythenearestclosingbasepair•  Theseenergiesareestimatedexperimentallyfromsmall

syntheticRNAs.

•  Positiveenergy-addedforlowentropyregionssuchasbulges,loops,etc.

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RNASecondaryStructure

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Hairpin loop

NearestNeighborModel

•  Hairpinenergy:•  Experimentallymeasuredforhairpinsoflength5,6,7,8,…

uptoamaximum.Extrapolationabovethemaximum.

•  Theclosingpairaffectstheenergy.DistinguishbetweenA-UandC-G.

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RNASecondaryStructure

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Bulge Loop

Internal Loop

NearestNeighborModel

•  Bulge/Internalenergy:•  LetL1,L2denotethelengthsofthetwosidesofthebulge/

internalloop.

•  ExperimentallymeasuredfordifferentvaluesofL1,L2.

•  Inpracticeforcomputationalconvenience,theenergyisgivenasfunctionofL1+L2byalookuptableandextrapolation.

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RNASecondaryStructure

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Junction (Multiloop)

NearestNeighborModel

•  Multiloopenergy:•  LetUdenotethenumberofunpairedbases.

•  LetPdenotethenumberofbasepairs.•  ThefreeenergyisanaffinefunctionofUandP:

a1 + a2 U + a3 P.

•  ThisistheleastaccuratecomponentoftheNNmodel.

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