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[q%o JK[Bߒ֎ +TA8[ Vv\Go[:jz֑u𷮵o+[0P;"m-;AvqohۋL=Ԏ!{oOkA`vD;Z;."w(G;q7i 5ֱek:IWiހUY#ҷp>R}w54p ;CP$5$q \) W!Wpry.9rCu׺k!-0?sZuK +aJ87p[re \ W!g,\C+k:* Cd*9*Cn;jZCc8zCk`8FC.! i8% \ W"b.syE?%ON{!)ŌO( 'j  F$RNA Structure Logo\http://www.cbs.dtu.dk/gorodkin/appl/slogo.html Circle Graphxhttp://bioinfo.math.rpi.edu/~mfold/sir_doc/circle_graph.html.Free Energy Calculationhttp://bioinfo.math.rpi.edu/~mfold/mfold/02Mar27-07-50-49.out.html0STRUCTURE_1"Display Structure|http://bioinfo.math.rpi.edu/~mfold/mfold/02Mar27-07-50-49.htmlUWorksheet Excel.Sheet.802Microsoft Excel Worksheet#XWorksheet Excel.Sheet.802Microsoft Excel Worksheet2ZWorksheet Excel.Sheet.802Microsoft Excel Worksheet0aWorksheet Excel.Sheet.802Microsoft Excel WorksheetD,Michael Zucker's MFOLD^http://bioinfo.math.rpi.edu/~mfold/rna/fold.cgiEHRNABase: The RNA Structure Database.http://www.rnabase.org/FRNA databases\http://megasun.bch.umontreal.ca/other/rna.html/ 0DTimes New Roman(0(z[ 0 DArialNew Roman(0(z[ 0 " DArial Blackman(0(z[ 0 "0DVerdanaackman(0(z[ 0 "@DWingdingskman(0(z[ 0 PDArial Unicode MS0(z[ 0 " A .  @n?" dd@  @@`` @gp[   !')+%7VX 9F/=B DHJLN-/# 08.*,  "$&(:G15 63YWOMKIEC>42?@ APRQS<V ;TU+Z]%?Db$-30c ?"Fb$Y+?iSń=$KFb$ w=W8sg 6b$3hFhH?ݳ{ b$ ڦtqҴW6eDa b$ԃ(s^ f }b$%jVc 8}*ab$ZfbT^b$)/d@K.]$b$p8̗ ":ZQb$IY7FYvG}b$ןxjK,\*9i1s[!"$ɧå&"$P tqƕE'b +b$[nQ/@sA?8"$(oBء px$"$͋6"᝖j΄S| Q 0AA 3@8<R ʚ;U_8ʚ;g42d2d@z[ 0xppp@ <4!d!dl 0<4ddddl 0<4ddddl 0D g4KdKd@z[ 0Tp@ ppJ0___PPT10  ___PPT9 DEFz? %O =5"RNA Secondary Structure Prediction##0 OutlineReview: RNA v DNA Predicting RNA secondary structure Features of RNA secondary structure Assumptions Methods of RNA structure prediction 0 xReviewWhat is RNA RNA vs. DNA RNA is ribonucleic acid, closely related to deoxyribonucleic acid or DNA. RNA is the only biological polymer that serves as both a catalyst (like proteins) and as information storage (like DNA). RNA is structurally very similar to DNA with three main differences:  %! The DNA base Thymine is replaced by Uracil in RNA. This makes the RNA alphabet A, C, G, U rather than the DNA alphabet A, C, G, T. The phosphate sugar backbone of RNA is built out of ribose instead of deoxyribose. RNA is synthesized as a single stranded molecule.      %Each ribonucleotide contains a phosphate group a sugar group (ribose) a base The polymer is formed by the linkage of the phosphate groups. The non-planar 5 member ribose ring connects the phosphate to the base. Finally, the bases are connected to the ribose group. Only the bases differ. LZZ Z    Four Bases in RNA:  Three Major Types of RNA:messenger RNA (mRNA), serves as a temporary copy of genes that is used as a template for protein synthesis transfer RNA (tRNA), serves as adaptor molecules that decode the genetic code ribosomal RNA (rRNA), serves as catalyst for the synthesis of proteins U:1 U:2    Other Types of RNA:There are a number of other types of RNA present in smaller quantities as well: small nuclear RNA (snRNA) small nucleolar RNA (snoRNA) 4.5S signal recognition particle (SRP) RNA. 8PdPd "Predicting RNA Secondary Structure##TWhat is RNA structure prediction? Why we study RNA structure prediction Terminology *T T" *What Is RNA Secondary Structure Prediction++RNA sequence folds into functional shape by pairing complementary bases Canonical base pairs: complementary bases, C-G and A-U form stable base pairs Watson-Crick pairs G-U wobble pair ^8H -      &" "Why Study RNA Structure Prediction##=Secondary structure related to function Drug, viral research  'Terminology of RNA Secondary Structures((Stacked pairs Base-pairing/base-stacking interactions. Usually Watson-Crick pairs, but G-Us are not uncommon, and other noncanonical pairs do occur Hairpin Loop Bulge Loop Interior Loop <ZZ'Z' Multi-loop Pseudoknots often not considered to be "secondary structure --most RNA secondary structure algorithms ignore them 6gg  #$Features of RNA Secondary Structure:%%(Intermediate step to 3-D structure Double-stranded regions formed by single-stranded molecule folding back on itself Downstream run of bases must be complementary to upstream run of bases so Watson-Crick pairing can occurZ$ Features (Continued)(G-C base pairs contribute greatest energy stability. A-U base pairs contribute less stability. G-U base pairs (wobble pairs) contribute least stability.$n@# Assumptions: That the most likely structure is similar to the most energetically stable structure. The energy associated with a particular base pair in a double-stranded region is influenced only by the previous base pair. The structure is to be formed in a manner that does not produce any knots. ( D%Representation of Assumptions: *Draw sequence in circular form Paired bases joined by arcs If structure to be free of knots, none of the arcs must cross (If lines cross, psuedoknot)B$  #Methods of RNA Structure Prediction$$uDot Matrix Sequence Comparison Minimum Free Energy MFOLD Covariation Analysis of RNA Sequences Context-Free Grammars< W WDot Matrix Sequence ComparisonvFind stretches of self-complementary regions Visual representation is easy to evaluate No need to compensate for gaps g*h+ Weaknesses: No "score , evaluation produced For long sequences, too slow for a database search Doesn't actually align sequences Minimum Free EnergyEvery base compared to every other base, similar to dot matrix analysis Diagonal indicates potential double-stranded area Sum negative base-stacking energies for each pair bases in diagonal Add estimated positive energies for loopsZS&Predicted Free-Energy Values (kcal/mole at 37 degrees C) for base pair and other features of predicted RNA secondary structures &$ V' Free Energy Calculation   U 0MFOLD (Michael Zucker)Predicts non-based-paired interactions Predicts several structures having energies close to minimum free energy Accurately depict structures of RNA molecules derived from comparative sequence analysis  Representations of MFOLDBDisplay Structure Most widely used. Closest to physical structure&11U 0Limitations of MFOLD;Does not compute all structures within a given energy range of the minimum free-energy structure. No alternative structures are produced that have the absence of base pairs in the best structure If two sub-structures are joined by a stretch of unpaired bases, no structures are produced that are suboptimal for both*bZZb!%Covariation Analysis of RNA Sequences&&Based on information theory applied to biology After transcription, RNA spliced by cell Splicing done at donor and receptor sites Height of stack shows degree of conservation proportional to frequency in acceptors RNA Structure Logo "Z ZU 0"Structure Logo [(Needs multiple alignment of a family of RNA to identify columns of high information contents These columns indicate conservation which is essential in secondary structure and base pairing > ]^ \)'Stochastic Context Free Grammars (SCFG)((Each RNA structure can be specified by a stochastic context-free grammar like that for a programming language This can be used to describe and classify RNAs Models can be used to search the DNA genome for RNA genes.   k, Productions m-n/q0o.SummaryMethods include Analysis of all possible combinations of potential double-stranded regions by energy minimization methods Identification of base covariation that maintains secondary (and tertiary) structure of RNA during evolution& References Mount, Daniel W., Bioinformatics Sequence and Genome Analysis, Cold Spring Harbor Laboratory Press, 2001 M. Zuker, P. Stiegler (1981) Optimal computer folding of large RNA sequences using thermodynamic and auxiliary information, Nucl Acid Res 9: 133-148 J. Gorodkin, L. J. Heyer, S. Brunak and G. D. Stormo. Displaying the information contents of structural RNA alignments: the structure logos. Comput. Appl. Biosci., Vol. 13, no. 6 pp 583-586, 1997. T. D. Schneider and R. M. Stephens. Sequence logos: a new way to display consensus sequences. Nucleic Acids Research, Vol. 18, no. 20, pp 6097-6100, 1990. Yizong Cheng, University of Cincinnati, RNA Secondary Structure, cheng.ececs.uc.edu Chen, R. O., Felciano, R., and Altman, R. B.1997. RIBOWEB: Linking structural computation to a Knowledge Base of published experimental data, Ismb 5:84  87. W+M_9?(b,bbb bbBRNA Structure DatabasesIMichael Zucker's MFOLD RNABase: The RNA Structure Database RNA databases< DU 0EU 0;FU 0<I/|()*+,-./01 2 3 4 5 6789:;<=>CGHIJLMN O!P"Q#R$T%W&]'^(l)p*  ` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@,? 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Rather, intra-strand base pairing will produce structures such as the one shown below: 8Jm l  `  <0 P   5 3 G A G A G A G A G A G A G A G A U C U C U C U C U C U C U C U C U C _]H  0޽h ? ̙33  PH6(  H H 0 P   r H S  @`  H H 0޽h ? ̙33  p<6(  < < 0H Pp   r < S   PPpp  H < 0޽h ? ̙33  @6(  @ @ 0P P   r @ S  @`  H @ 0޽h ? ̙33  NFD(  DP D 6W Display of RNA Secondary Structures D$g $tcN D C &A img26nH D 0޽h ? ̙33  6(    0 P   r  S ( @`  H  0޽h ? ̙33  6(    0ܼ P   r  S  @`  H  0޽h ? ̙33 $ 6(    0LŚ P   r  S  ƚ @`  H  0޽h ? ̙33 # 0 6(      0ʚ P   r   S ˚ @`  H   0޽h ? ̙33  P T(    <h՚ (0  P Circle Graph U 0 X  0A ? `H  0޽h ? ̙33  pL6(  L L 04 P   r L S     H L 0޽h ? ̙33  \6(  \ \ 0 P   r \ S d @`  H \ 0޽h ? ̙33p)  P`(  `x ` <A 0??@8 0H ` 0޽h ? ̙33  d6(  d d 04 P   r d S  @`  H d 0޽h ? ̙33 " h6(  h h 0X  P   r h S ,  @`  H h 0޽h ? ̙33 % @<(  @x @ <A ??@>  @ 0T p@   H @ 0޽h ? ̙33& ` HS(  H\ H C 4A ch5_stemloopPP zx H <A #??@  #  H 0C  P   ? For Figure:  x  H <A 2?? 0H< 2H H 0޽h ? ̙33 !   l"(  lr l S       l 6 @P  dIn the structure, there are five U's in the hairpin loop region, which has a predicted destabilizing energy of +4.4 kcal/mol. Therefore, the total free energy reduction predicted for the molecule given the above secondary structure is: -9.8 kcal/mol + 4.4 kcal/mol = -5.4 kcal/mol0 2 L  l# PH l C N  l N l S >  l s *' A/U followed by G/C = -1.7 kcal/mol G/C followed by C/G = -3.4 kcal/mol C/G followed by C/G = -2.9 kcal/mol C/G followed by A/U = -1.8 kcal/mol sum = -9.8 kcal/mol H l 0޽h ? ̙33   @p6(  p p 01 P   r p S 2 @`  H p 0޽h ? ̙33c   ``(  `R ` s *VVX ` 0A ?00 3 ` <X:4  EEnergy Dot Plot$H ` 0޽h ? ̙33  t6(  t t 0@ P   r t S A @`  H t 0޽h ? ̙33  x6(  x x 0XG P   r x S ,H @`  H x 0޽h ? ̙33  6(    0T P   r  S U @`  H  0޽h ? ̙33  x(    0a P   L  C $A07O 2H  0޽h ? ̙33 ' P6(  P P 0e P   r P S f p  H P 0޽h ? ̙33 (  T6(  T T 0xk P   r T S Ll @`  H T 0޽h ? ̙33  d\@t(  t t 0(t     D t 0~@P P = { S0 S1, S7 G S8, S1 C S2 G, S8 G, S2 A S3 U, S9 A S10 U, S3 S4 S9, S10 G S11 C, S4 U S5 A, S11 A S12 U, S5 C S6 G, S12 U S13, S6 A S7 S13 C }            t <`wm x"For sequence CAUCAGGGAAGAUCUCUUG:# H t 0޽h ? ̙33 px>(  xR x 0|S t  S0 S1 CS2G CAS3UG CAS4S9UG CAUS5AS9UG CAUCS6GAS9UG CAUCAS7GAS9UG CAUCAGS8GAS9UG CAUCAGGGAS9UG CAUCAGGGAAS10UUG CAUCAGGGAAGS11CUUG CAUCAGGGAAGAUS13UCUUG CAUCAGGGAAGAUCUCUUG     x <X p @ Derivation H x 0޽h ? ̙33 zr %* (  V  0Ђ  S0 S1 S2 S3 S4 S9 S5 S10 S6 S11 S7 S12 S8 S13 C A U C A G G G A A G A U C U C U U G     BLB  c $D`p p PLB  c $Dp p LB @ c $Dp p LB  c $D  @LB   c $D  @LB   c $D` LB   c $D` LB   c $D  LB   c $D 0 LB  c $D  LB  c $D  LB  c $D0 ` LB @ c $D p`@LB @ c $DpLB @ c $D @LB  c $D pLB  c $D0 ` LB @ c $D0 `@LB  c $D  @LB  c $DLB  c $D0 LB  c $D0 @LB @ c $Dp @LB @ c $D @LB @ c $D ` pLB  @ c $D0 P pLB ! c $D`LB # c $D @@LB $ c $D @LB % c $DP@LB & c $Dp@pLB ' c $D 0LB ( c $D0 LB ) c $D LB * c $D pH  0޽h ? ̙33U $U(    6P MS0 | S1 C | G S2 A | U S3 U U S4 S9 C A A S5 S10 C A S6 G G S11 U A S7 S12 S13 G S8 U C G -)                       LB @ c $D` LB  c $D`@ ` LB @ c $D LB   c $D@ LB  @ c $D LB   c $D LB  @ c $D@ 0 LB  c $D @0 LB  c $D P LB  c $Dp @` LB  c $D` p  LB @ c $D0  LB  c $D@ 0 LB  c $D0  LB @ c $D p LB  c $D @@LB  c $DP P LB  c $D 0 LB  c $D  LB  c $DP LB  c $D` LB @ c $D pLB @ c $D  LB  c $D  LB   c $D0 p 0 LB !@ c $D 0  LB #@ c $D PP LB $ c $D @ H  0޽h ? ̙3380___PPT10.84: * P|6(  | | 0p P   r | S D @`  H | 0޽h ? ̙33  `P6(  P P 0P P   r P S $ @`  H P 0޽h ? ̙33  T6(  T T 0 P   r T S  @`  H T 0޽h ? ̙33  0 um(  X  C    m  S     In RNA, guanine and cytosine pair (GC) by forming a triple hydrogen bond, and adenine and uracil pair (AU) by a double hydrogen bond; additionally, guanine and uracil can form a single hydrogen bond base pair. The stability of a particular secondary structure is a function of several constraints: The number of GC versus AU and GU base pairs. (Higher energy bonds form more stable structures.) The number of base pairs in a stem region. (Longer stems result in more bonds.) The number of base pairs in a hairpin loop region. (Formation of loops with more than 10 or less than 5 bases requires more energy.) The number of unpaired bases, whether interior loops or bulges. (Unpaired bases decrease the stability of the structure.) The stability of a secondary structure is quantified as the amount of free energy released or used by forming base pairs. Positive free energy requires work to form a configuration; negative free energies release stored work. Free energies are additive, so one can determine the total free energy of a secondary structure by adding all the component free energies (units are kilocalories per mole). The more negative the free energy of a structure, the more likely is formation of that structure, because more stored energy is released. This fact is used to predict the secondary structure of a particular sequence. Discovering a base pair configuration with the minimum possible free energy is the goal of most secondary structure prediction algorithms.  H  0޽h ? ̙33 0 G(  X  C      S     ICCAGAGGCCCAACUGGUAAACGGGCCCGAAGCUCAACGGGAUAAUGAGCC CGAAGCCGAACGGGAAAACCGGCCCCAAGCGCAGGGGAGAAGCGCCCGAC GCCAACGGGAGAAUGGCCCGUUUUCAGUCGGGAAAAACUGACCGUUACUC CUCGGGAUAAAGGAGCCGUAAGAGGACGGGAUAAACCUCCCGUAGGAGGC GGGAUAUCUCCCCGUGCCGGCGGGAUAUCGGCCCGAACUCGACGGGAUAA CGAGCCGACUCGCGGGAUAACGAG H  0޽h ? ̙33 0 zr (  X  C    r  S  @   H  0޽h ? ̙33  0 h(  X  C      S  @   j:A multi-loop is a loop that contains more than two base pairs. There is also an external or closing loop, where one base pair in the loop is closes to the ends of the RNA strand. All other pairs are interior. The external loop is the one that maximized j  i over i, j in the loop. H  0޽h ? ̙33s 0 3+(  X  C    +  S  @   The stacking energy of the base pairs provides increased energy stability. Single-stranded regions destabilize neighboring double-stranded regions.H  0޽h ? ̙33 0 zr (  X  C    r  S ,  @   H  0޽h ? ̙33 0 zr (  X  C    r  S 4" @   H  0޽h ? ̙33 0 zr (  X  C    r  S ' @   H  0޽h ? ̙33V 0 (  X  C      S , @   xIt is widely believed, because of the dual function of RNA, that life began with RNA and proteins and DNA evolved later.yyH  0޽h ? ̙33! 0 zr  (  X  C    r  S |  @   H  0޽h ? ̙33  0 @Z(  X  C      S 4 @   \,The difference between DNA and RNA backbones--H  0޽h ? ̙33 0 zr` (  X  C    r  S 0; @   H  0޽h ? ̙33F 0 (  X  C      S X@ @   hRNA backbone Uracil in RNA instead of Thymine in DNA55H  0޽h ? ̙33- 0 }(  X  C      S (G @   OCanonical base pairs: GC, AU, GU The number of GC versus AU and GU base pairs.PPH  0޽h ? ̙33 0 zr (  X  C    r  S O @   H  0޽h ? ̙33  0 ZR(  X  C    R  S S @   --snRNA-- RNA splicing apparatus in nucleus, not translated, found only in eurkaryotes --snoRNA-- a spherical body of the nucleus of most eukaryotes that becomes enlarged during protein synthesis, is associated with a nucleolus organizer, and contains the DNA templates for ribosomal RNA Within the nucleus are one or more nucleoli. The nucleolus is roughly spherical, and appears as a mass of densely stained granules and fibers under an electron microscope. It consists of nucleolar organizers. They are specialized regions of some chromosomes with multiple copies of genes for ribosome synthesis, along with a considerable amount of RNA and proteins representing ribosomes in various stages of production. An average, healthy cell can produce up to 10 000 ribosomes per minute. The nucleolus is organized from the "nucleolar organizing regions" on different chromosomes. A number of chromosomes get together and transcribe ribosomal RNA at this site. Within the nucleus are found chromatin and a structure called the nucleolus. Chromatin is DNA in its active form. It consists of DNA looped around histone proteins. The nucleolus is a knot of chromatin. It is the nucleolus that manufactures ribosomes  H  0޽h ? ̙33  0 zr (  X  C    r  S i @   H  0޽h ? ̙33h  0 (  (  X  C       S r @   Single-stranded RNA forms structure driven by hydrogen bonding and stacking of bases. C-G 3 hydrogen bonds A-U 2 hydrogen bonds G-U wobbleH  0޽h ? ̙33" 0 zr@ (  X  C    r  S L{ @   H  0޽h ? ̙33[ 0 `(  X  C      S t @   }Because the secondary structure is related to the function of the RNA, we want to be able to predict the secondary structure.~~H  0޽h ? ̙33f  0 &(  X  C      S $ @   A hairpin loop contains exactly one base pair, with the loop at least four bases long. An interior loop contain exactly two base pairs A bulge is an internal loop with one base from each of its two base pairs adjacent on the backbone A stacked pair is a loop formed by two base pairs (i, j) and (i +1), ( j  1), having both ends adjacent on the backbone. This is the only type of loop that stabilizes the structure. All other loops are destabilizing.H  0޽h ? ̙33 0 !(  X  C      S  @   #Self-complementary regions appear as rows of dots going from upper left to lower right. A/U, G/C, not G/U visual representation is easy to evaluate don't have to deal with gaps doesn't produce a "score" too slow for a database search doesn't actually align sequences H  0޽h ? ̙33 0 F>p(  X  C    >  S     ~Energy dot plot In the upper triangular region, a dot in row i and column j represents a base pair between the ith and jth bases. The black dots represent all the optimal foldings. The colored, smaller dots represent the superposition of all possible suboptimal foldings within p% of the minimum free energy, where p is the maximium percent deviation from the minimum free energy. The color ranges are red, blue and yellow; representing base pairs that are in foldings within p/3%, 2p/3% and p% of the minimum free energy, respectively. Thus the yellow dots represent base pairs that are least likely to form. CCAGAGGCCCAACUGGUAAACGGGCCCGAAGCUCAACGGGAUAAUGAGCC CGAAGCCGAACGGGAAAACCGGCCCCAAGCGCAGGGGAGAAGCGCCCGAC GCCAACGGGAGAAUGGCCCGUUUUCAGUCGGGAAAAACUGACCGUUACUC CUCGGGAUAAAGGAGCCGUAAGAGGACGGGAUAAACCUCCCGUAGGAGGC GGGAUAUCUCCCCGUGCCGGCGGGAUAUCGGCCCGAACUCGACGGGAUAA CGAGCCGACUCGCGGGAUAACGAG *S- $  #u H  0޽h ? ̙33$ 0 sk`(  X  C    k  S  P   Draw the sequence in circular form. The paired bases are then joined by arcs. If the total structure with all predicted base pairs is to be free of knots, none of the arcs must cross CCAGAGGCCCAACUGGUAAACGGGCCCGAAGCUCAACGGGAUAAUGAGCC CGAAGCCGAACGGGAAAACCGGCCCCAAGCGCAGGGGAGAAGCGCCCGAC GCCAACGGGAGAAUGGCCCGUUUUCAGUCGGGAAAAACUGACCGUUACUC CUCGGGAUAAAGGAGCCGUAAGAGGACGGGAUAAACCUCCCGUAGGAGGC GGGAUAUCUCCCCGUGCCGGCGGGAUAUCGGCCCGAACUCGACGGGAUAA CGAGCCGACUCGCGGGAUAACGAG H  0޽h ? ̙33 0 zr (  X  C    r  S  @   H  0޽h ? ̙33 0 zrp (  X  C    r  S  @   H  0޽h ? ̙33 0 d\(  X  C    \  S   @   The height of each stack of letters is in bits, and shows how conserved that position is. The height of each genetic letter (A, C, G or T) is proportional to its frequency in the acceptors. H  0޽h ? ̙33 0 H(  X  C      S  @   JUses a set of homologous, aligned sequences to identify evolutionary conserved structure and identify covarying residues in the sequence. After transcription, pieces are cut from the RNA in a process called splicing; the splicing points are called donor and acceptor splice sites. H  0޽h ? ̙33 0 zr$ (  $X $ C    r $ S  @   H $ 0޽h ? ̙33 0 (!(  (X ( C     ( S  @   #AGCCAUUUUUUGGCUH ( 0޽h ? ̙33 0 zrP, (  ,X , C    r , S L @   H , 0޽h ? ̙33 0 zr00 (  0X 0 C    r 0 S  @   H 0 0޽h ? ̙33f 0 &4(  4X 4 C     4 S d @   Book says  row of matches in RNA matrix Book also says upper right to lower left& H 4 0޽h ? ̙33% 0 zr@8 (  8X 8 C    r 8 S   @   H 8 0޽h ? ̙33# 0 zr < (  <X < C    r < S  @   H < 0޽h ? ̙33& 0 D!(  DX D C     D S x @   #AGCCAUUUUUUGGCUH D 0޽h ? ̙331' 0 L(  LX L C     L S  @   M Regions that are not complementary have a destabilizing effect on the total free energy of a structure and have different predicted values based on the types and lengths of the structures they form. In the above structure, there are five U's in the hairpin loop region, which has a predicted destabilizing energy of +4.4 kcal/molNNH L 0޽h ? ̙33( 0 nfX(  XX X C    f X S p& @   Needs multiple alignment of a family of RNA to identify columns of high information contents These columns indicate conservation which is essential in secondary structure and base pairing (]^ H X 0޽h ? ̙33{) 0 ;30\(  \X \ C    3 \ S X2 @   Each RNA structure can be specified by a stochastic context-free grammar like that for a programming language This can be used to describe and classify RNAs  H \ 0޽h ? ̙33* 0 p!(  pX p C     p S |: @   #AGCCAUUUUUUGGCUH p 0޽h ? ̙33\. 0 l(  X  C      S  @   nZEnergy minimization methods are so well refined that a series of energetically feasible models and the most thermodynamically probable structures may be computed. Covariation analysis (by C. Woese, 1983) led to his building detailed structural models for rRNAs. 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