RNAs

RNA Basics transfer RNA (tRNA) transfer RNA (tRNA) messenger RNA (mRNA) messenger RNA (mRNA) ribosomal RNA (rRNA) ribosomal RNA (rRNA) small interfering RNA (siRNA) small interfering RNA (siRNA) micro RNA (miRNA) micro RNA (miRNA) small nucleolar RNA (snoRNA) small nucleolar RNA (snoRNA)

Pre-miRNA

tRNA Yeast phenylalanine transfer RNA Yeast phenylalanine transfer RNA Yeast phenylalanine transfer RNA Yeast phenylalanine transfer RNA Codons : UUU, UUC Codons : UUU, UUC Phenylalanine : Phenylalanine :

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RNA Basics RNA bases A,C,G,U RNA bases A,C,G,U Canonical Base Pairs Canonical Base Pairs A-U A-U G-C G-C G-U G-U “wobble” pairing Bases can only pair with one other base. Bases can only pair with one other base. 2 Hydrogen Bonds 3 Hydrogen Bonds – more stable

Pairing between tRNA's anticodon and mRNA's codon

The non-standard base pairing at the wobble position

RNA Secondary Structure Hairpin loop Junction (Multi-branched loop) Bulge Loop Single-Stranded Interior Loop Stem Pseudoknot

RNA evolution is constrained by structure Consensus binding site for R17 phage coat protein (. Consensus binding site for R17 phage coat protein (translational repressor). N = {A, C, G, U} N = {A, C, G, U} Y = {C, U}, pyrimidines (1 ring) Y = {C, U}, pyrimidines (1 ring) R = {A, G}, purines (2 rings) R = {A, G}, purines (2 rings) N’ = complement {N} N’ = complement {N}

Sequence Alignment as a method to determine structure Bases pair in order to form backbones and determine the secondary structure Bases pair in order to form backbones and determine the secondary structure Aligning bases based on their ability to pair with each other gives an algorithmic approach to determining the optimal structure Aligning bases based on their ability to pair with each other gives an algorithmic approach to determining the optimal structure

RNA folding RNA sequence RNA sequence i j i j j  1 i +1

Base Pair Maximization - Nussinov- Jacobson Folding Alg (DP) Base pair at i and j Unmatched at iUmatched at jBifurcation 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 i j j  1 i +1  (i,j) = 1 (i,j pairs), 0 o.w. ?

Base Pair Maximization - Nussinov- Jacobson Folding Alg (DP) i j j i

i, ji, j-1 i+1, ji+1, j-1 i j i j

Alignment Method Alignment Method Align RNA strand to itself Align RNA strand to itself Score increases for feasible base pairs Score increases for feasible base pairs Each score independent of overall structure Each score independent of overall structure Bifurcation adds extra dimension Bifurcation adds extra dimension Initialize first two diagonal arrays to 0 Fill in squares sweeping diagonally Bases cannot pair, similar to unmatched alignment S(i, j – 1) Bases can pair, similar to matched alignment S(i + 1, j) Dynamic Programming – possible paths S(i + 1, j – 1) +1 Base Pair Maximization – Nussinov- Jacobson Folding Alg (DP)

Alignment Method Alignment Method Align RNA strand to itself Align RNA strand to itself Score increases for feasible base pairs Score increases for feasible base pairs Each score independent of overall structure Each score independent of overall structure Bifurcation adds extra dimension Bifurcation adds extra dimension Initialize first two diagonal arrays to 0 Fill in squares sweeping diagonally Reminder: For all k S(i,k) + S(k + 1, j) k = 1 : Bifurcation max in this case S(i,k) + S(k + 1, j) Reminder: For all k S(i,k) + S(k + 1, j) Bases cannot pair, similar Bases can pair, similar to matched alignment Dynamic Programming – possible paths Bifurcation – add values for all k Base Pair Maximization – Nussinov- Jacobson Folding Alg (DP)

Base Pair Maximization - Drawbacks Base pair maximization will not necessarily lead to the most stable structure Base pair maximization will not necessarily lead to the most stable structure May create structure with many interior loops or hairpins which are energetically unfavorable May create structure with many interior loops or hairpins which are energetically unfavorable Comparable to aligning sequences with scattered matches – not biologically reasonable Comparable to aligning sequences with scattered matches – not biologically reasonable

Energy Minimization Thermodynamic Stability Thermodynamic Stability Estimated using experimental techniques Estimated using experimental techniques Theory : Most Stable is the Most likely Theory : Most Stable is the Most likely No Pseudoknots due to algorithm limitations No Pseudoknots due to algorithm limitations Uses Dynamic Programming alignment technique Uses Dynamic Programming alignment technique Attempts to maximize the score taking into account thermodynamics Attempts to maximize the score taking into account thermodynamics

Equilibrium free energy  G for RNA structure Freier, et al, 1986

Energy Minimization Results Linear RNA strand folded back on itself to create secondary structure Circularized representation uses this requirement Arcs represent base pairing All loops must have at least 3 bases in them All loops must have at least 3 bases in them Equivalent to having 3 base pairs between all arcs Equivalent to having 3 base pairs between all arcs Exception: Location where the beginning and end of RNA come together in circularized representation

Trouble with Pseudoknots Pseudoknots cause a breakdown in the Dynamic Programming Algorithm. In order to form a pseudoknot, checks must be made to ensure base is not already paired – this breaks down the recurrence relations

Energy Minimization Drawbacks Compute only one optimal structure Compute only one optimal structure Usual drawbacks of purely mathematical approaches Usual drawbacks of purely mathematical approaches Similar difficulties in other algorithms Similar difficulties in other algorithms Protein structure Protein structure Exon finding Exon finding