#16 - Profiles & HMMs 9/28/07

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1 # - Profles & HMMs 9/28/7 BCB 444/544 Lecture Profles & Hdden Markov Models (HMMs) #_Sept28 Requred Readng (before lecture) Mon & Wed Sept 24 & 2- Lecture 4 & 5 Revew: Nucleus, Chromosomes, Genes, RNAs, Protens Surprse lecture: No assgned readng Fr Sept 28 - Lectures Profles & Hdden Markov Models Chp - pp Eddy: What s a hdden Markov Model? 24 Nature Botechnol 22:35 Thurs Sept 27 - Lab 4 & Mon Oct - Lecture 7 Proten Famles, Domans, and Motfs Chp 7 - pp 85-9 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 2 Assgnments & Announcements BCB Extra Requred Readng Fr Sept 2 Exam - Graded & returned n class - Really! HW#2 - Graded & returned n class - Really! Answer KEYs posted on webste Grades posted on WebCT HomeWork #3 - posted onlne Due: Mon Oct 8 by 5 PM HW544Extra # - posted onlne Due: Task. - Mon Oct by noon Task.2 & Task 2 - Mon Oct 8 by 5 PM Mon Sept 24 BCB 544 Extra Requred Readng Assgnment: Pollard KS, Salama SR, Lambert N, Lambot MA, Coppens S, Pedersen JS, Katzman S, Kng B, Onodera C, Sepel A, Kern AD, Dehay C, Igel H, Ares M Jr, Vanderhaeghen P, Haussler D. (2) An RNA gene expressed durng cortcal development evolved rapdly n humans. Nature 443: do:.38/nature53 PDF avalable on class webste - under Requred Readng Lnk BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 3 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 4 Extra Credt Questons #2-: 2. What s the sze of the dystrophn gene (n kb)? Is t stll the largest known human proten? 3. What s the largest proten encoded n human genome (.e., longest sngle polypeptde chan)? 4. What s the largest proten complex for whch a structure s known (for any organsm)? 5. What s the most abundant proten (naturally occurrng) on earth?. Whch state n the US has the largest number of moble genetc elements (transposons) n ts lvng populaton? For pt total (.2 pt each): Answer all questons correctly & submt by to terrble@astate.edu For 2 pts total: Prepare a PPT slde wth all correct answers & submt to ddobbs@astate.edu before 9 AM on Mon Oct Choose one opton - you can't earn 3 pts! Partal credt for ncorrect answers? only f they are truly amusng! BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 5 Extra Credt Questons #7 & #8: Gven that each male attendng our BCB 444/544 class on a typcal day s healthy (let's assume M H =7), and s generatng sperm at a rate equal to the average normal rate for reproductvely competent males (ds p /dt =? per mnute): 7a. How many rounds of meoss wll occur durng our 5 mnute class perod? 7b. How many total sperm wll be produced by our BCB 444/544 class durng that class perod? 8. How many rounds of meoss wll occur n the reproductvely competent females n our class? (assume F H =5) For. pts total (.2 pt each): Answer all questons correctly & submt by to terrble@astate.edu For pts total: Prepare a PPT slde wth all correct answers & submt to ddobbs@astate.edu before 9 AM on Mon Oct Choose one opton - you can't earn more than pt for ths! Partal credt for ncorrect answers? only f they are truly amusng! BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 BCB 444/544 Fall 7 Dobbs

2 # - Profles & HMMs 9/28/7 Informaton flow n the cell? Modelng Metabolc Pathways? see MetNet DNA -> RNA -> proten: Replcaton = DNA to DNA - by DNA polymerase Transcrpton = DNA to RNA - by RNA polymerase Translaton = RNA to proten - by rbosomes Exceptons/Complcatons: DNA rearrangements: (by moble genetc elements, recombnaton) Reverse transcrpton: (RNA -> DNA, by reverse transcrptase) Post-transcrptonal modfcatons: RNA splcng (removal of ntrons, by splceosome) RNA edtng (addton/removal of nucleotdes - usually U's) Post-translatonal modfcatons: Proten processng BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 7 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 8 Chromosomes & Genes Gene regulaton Transcrptonal regulaton s prmarly medated by protens that bnd cs-actng elements or DNA sequence sgnals assocated wth genes: DNA level (sequence-specfc) regulatory sgnals Promoters, termnators Enhancers, repressors, slencers Chromatn level (global) regulaton Heterochromatn (nactve) e.g., X-nactvaton n female mammals Genes n chromatn are not just beads on a strng they are packaged n complex structures that we don't yet fully understand In eukaryotes, genes are often regulated at other levels: Post-transcrptonal (RNA transport, splcng, stablty) Post-translatonal (proten localzaton, foldng, stablty) BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 9 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 Promoter = DNA sequences requred for ntaton of transcrpton; contan TF bndng stes, usually "close" to start ste Transcrpton factors (TFs) - protens that regulate transcrpton (In eukaryotes) RNA polymerase bnds by recognzng a complex of TFs bound at promotor Enhancer Enhancers & repressors = DNA sequences that regulate ntaton of transcrpton; contan TF bndng stes,can be far from start ste! Promoter RNAP = RNA polymerase II Frst, TFs must bnd TF bndng stes (TFBSs) wthn promoters; then RNA polymerase can bnd and ntate transcrpton of RNA ~2 bp Pre-mRNA Repressor Enhancers "enhance" transcrpton Repressors or slencers "repress" transcrpton -5, bp Gene Enhancer bndng protens (TFs) nteract wth RNAP Repressor bndng protens (TFs) block transcrpton BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 2 BCB 444/544 Fall 7 Dobbs 2

3 # - Profles & HMMs 9/28/7 Transcrpton factors (TFs) & ther bndng stes (TFBSs) Transcrpton factors - trans-actng factors - protens that ether actvate or repress transcrpton, usually by bndng DNA (va a DNA bndng doman) & nteractng wth RNA polymerase (va a "trans-actvatng doman) to affect rate of transcrpton ntaton Promotors, enhancers, and repressors - all contan bndng stes for transcrpton factors Promoters - usually located close to start ste; vs Enhancers/Slencers/Repressor sequences - can be close or very far away: located upstream, downstream or even wthn the codng sequence of genes!! "Non-codng" DNA? Many genes encode RNA that s not translated 4 Major Classes of RNA:. mrna = messenger RNA 2. trna = transfer RNA 3. rrna = rbosomal RNA 4. "Other" - Lots of these, dverse structures & functons: "Natural" RNAs: srna, mrna, prna, snrna, snorna, rbozymes Artfcal RNAs: RNA antsense RNA BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 3 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 4 RNA Sequence, Structure & Functon RNAs can have complex 3D stuctures (lke protens) & have many mportant functons n cellular processes Proten Sequence, Structure & Functon Amno acd sequence determnes proten structure But some protens need help foldng ("chaperones") n vvo Proten structure determnes functon But level, tmng & locaton of expresson are mportant Interactons wth other protens, DNA, RNA, & small lgands are also very mportant!! Rbosomes contan RNAs & protens Rbozymes are RNA enzymes capable of RNA cleavage RNA molecules are beleved to be precursors to DNA-based lfe Form complementary base pars and replcate (lke DNA) Perform enzymatc functons (lke protens) BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 5 We don't know the "foldng code" that determnes how protens fold! We don't know the "recognton code" that determnes how protens fnd and nteract wth correct partners! BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 A few Onlne Resources for: Cell & Molecular Bology NCBI Scence Prmer: What s a cell? NCBI Scence Prmer: What s a genome? BoTech s Lfe Scence Dctonary NCBI bookshelf Chp - Profles & Hdden Markov Models SECTION II Xong: Chp Profles & HMMs SEQUENCE ALIGNMENT Poston Specfc Scorng Matrces (PSSMs) PSI-BLAST TODAY: Profles Markov Models & Hdden Markov Models BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 7 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 8 BCB 444/544 Fall 7 Dobbs 3

4 # - Profles & HMMs 9/28/7 Algorthms & Software for MSA? #3 (NOT covered on Exam) Heurstc Methods - contnued Progressve algnments (Star Algnment, Clustal) Others: T-Coffee, DbClustal -see text: can be better than Clustal Match closely-related sequences frst usng a gude tree Partal order algnments (POA) Doesn't rely on gude tree; adds sequences n order gven PRALINE Preprocesses nput sequences by buldng profles for each Iteratve methods Idea: optmal soluton can be found by repeatedly modfyng exstng suboptmal solutons (eg: PRRN) Block-based Algnment Multple re-buldng attempts to fnd best algnment (eg: DIALIGN2 & Match-Box) Local algnments Profles, Blocks, Patterns - more on these soon! Applcatons of MSA Buldng phylogenetc trees Fndng conserved patterns: Regulatory motfs (TF bndng stes) Splce stes Proten domans Identfyng and characterzng proten famles Fnd out whch proten domans have same functon Fndng SNPs (sngle nucleotde polymorphsms) & mrna soforms (alternatvely splced forms) DNA fragment assembly (n genomc sequencng) BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 9 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 2 Applcaton: Dscover Conserved Patterns Patterns can also be represented as Sequence Logos Is there a conserved cs-actng regulatory sequence? Ratonale: f sequences are homologous (derved from a common ancestor), they may be structurally/functonally equvalent TATA box = transcrptonal promoter element Sequence Logo BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 2 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 22 Sequence Logo Sequence Logos: for Promoter elements (TF Bndng Stes) BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 23 Example was created from a set of TATA bndng stes from TRANSFAC database. Logo was created by WebLogo. Can see TATA-box qute easly. BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 24 BCB 444/544 Fall 7 Dobbs 4

5 # - Profles & HMMs 9/28/7 Sequence Logos - for RNA Splcng Stes Human ntron donor and acceptor stes BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 25 PSSM vs Profle PSI-BLAST Pseudocode Convert query to PSSM (or a Profle) do { BLAST database wth PSSM Stop f no new homologs are found Add new homologs to PSSM } Prnt current set of homologs Poston-Specfc Scorng Matrx: from ungapped MSA Profle: from MSA, ncludng gaps Note: Xong textbook dstngushes between PSSMs (whch have no gaps) & Profles (can nclude gaps). Thus, based on these defntons, PSI-BLAST uses a Profle to teratvely add new homologs - other authors refer to pattern used by PSI-BLAST as a PSSM. BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 2 What s a PSSM? Poston-Specfc Scorng Matrx A PSSM s: a representaton of a motf an n by m matrx, where n s sze of alphabet & m s length of sequence a matrx of scores n whch entry at (, j) s score assgned by PSSM to letter at the jth poston Xong: PSSM = table that contans probablty nformaton re: resdues at each poston of an ungapped MSA Also, sometmes called: Poston Weght Matrx (PWM) 2 letter alphabet A R N D C Q E G H I L K M F P S T W Y V BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/ resdue sequence gets -4 a score of I added more text to ths slde -4 3 K at poston 3 Note: Assumes postons are ndependent -4 2 PSSM Entres = Log-Odds Scores. Estmate probablty of observng each resdue (probablty of A gven M, where M s PSSM model) 2. Dvde by background probablty of observng each resdue (probablty of A gven B, where B s background model) 3. Take log so that can add (rather than multply) scores Observed frequency of resdue A & Pr log 2 $ % Pr Ths slde was modfed Foreground model (.e., the PSSM) ( A M )# ( A B)!! " Background model BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 28 Statstcs References Sequence Profles Statstcal Inference (Hardcover) George Casella, Roger L. Berger StatWeb: A Gude to Basc Statstcs for Bologsts Basc Statstcs: (correlatons, tests, frequences, etc.) Goal: to characterze sequences belongng to a class (structural or functonal) & determne whether a query sequence also belongs to that class DNA or RNA sequences Proten sequences Idea s to provde a "model" of the class aganst whch we can test the new sequence Electronc Statstcs Textbook: StatSoft (from basc statstcs to ANOVA to dscrmnant analyss, clusterng, regresson data mnng, machne learnng, etc.) BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 29 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 3 BCB 444/544 Fall 7 Dobbs 5

6 # - Profles & HMMs 9/28/7 Proten Sequence Profles & PSSMs Profle - a table that lsts frequences of each amno acd n each poston of a proten sequence PSSM - a specal type of Profle - wth no gaps Frequences are calculated from a MSA contanng a doman of nterest Can be used to generate a consensus sequence Derved scorng scheme can be used to algn a new sequence to the profle Profle can be used n database searches (PSI-BLAST) to fnd new sequences that match the profle Profles can also be used to compute MSAs heurstcally (e.g., progressve algnment) PSI-BLAST Lmtatons for generatng patterns or "motfs" Wth PSSMs, can't have nsertons and deletons Wth Profles, essentally 'add extra columns' to PSSM to allow for gaps Better approach (for defnng domans)? Profle HMM: elaborated verson of a profle Intutvely, a profle that models gaps BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 3 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 32 Sequence Motfs (Patterns) Types of representatons? HMMs: an example Nucleotde frequences n human genome Consensus Sequence Sequence Logo - "enhanced"consensus sequence, n whch symbol sze nformaton entropy Informaton entropy??? In nformaton theory, the Shannon entropy or nformaton entropy s a measure of the [decrease n] uncertanty assocated wth a random varable. Entropy quantfes nformaton n a pece of data. - Wkpeda Check out ths nterestng webste: Tom Schneder, NCIF A 2.4 C 29.5 T 2.5 G 29. PSSM - Poston-Specfc Scorng Matrx Profles HMMs - Hdden Markov Models BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 33 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 34 CpG Islands Hdden Markov Models - HMMs Wrtten CpG to dstngush from a C G base par) CpG dnucleotdes are rarer than would be expected from ndependent probabltes of C and G (gven the background frequences n human genome) Hgh CpG frequency s sometmes bologcally sgnfcant; e.g., sometmes assocated wth promoter regons ( start stes for genes) CpG sland - a regon where CpG dnucleotdes are much more abundant than elsewhere Goal: Fnd most lkely explanaton for observed varables Components: Observed varables Hdden varables Emtted symbols Emsson probabltes Transton probabltes Graphcal representaton to llustrate relatonshps among these BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 35 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 3 BCB 444/544 Fall 7 Dobbs

7 # - Profles & HMMs 9/28/7 The Occasonally Dshonest Casno An HMM for Occasonally Dshonest Casno A casno uses a far de most of the tme, but occasonally swtches to a "loaded" one Far de: Prob() = Prob(2) =... = Prob() = / Loaded de: Prob() = Prob(2) =... = Prob(5) = /, Prob() = ½ These are emsson probabltes Transton probabltes Prob(Far Loaded) =. Prob(Loaded Far) =.2 Transtons between states obey a Markov process (more on Markov chans/models/processes a bt later) BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 37 Transton probabltes Prob(Far Loaded) =. Prob(Loaded Far) =.2 Emsson probabltes Far de: Prob() = Prob(2) =... = Prob() = / Loaded de: Prob() = Prob(2) =... = Prob(5) = /, Prob() = ½ BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 38 The Occasonally Dshonest Casno Known: Structure of the model Transton probabltes Hdden: What casno actually dd FFFFFLLLLLLLFFFF... Observable: Seres of de tosses What we must nfer: When was a far de used? When was a loaded one used? Answer s a sequence FFFFFFFLLLLLLFFF... BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 39 HMM: Makng the Inference Model assgns a probablty to each explanaton for the observaton, e.g.: P(32 FFL) = P(3 F) P(F F) P(2 F) P(F L) P( L) = /.99 /. ½ Maxmum Lkelhood: Determne whch explanaton s most lkely Fnd path most lkely to have produced observed sequence Total Probablty: Determne probablty that observed sequence was produced by HMM Consder all paths that could have produced the observed sequence BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 4 HMM Notaton Calculatng Dfferent Paths to an Observed Sequence x = sequence of symbols emtted by model x = symbol emtted at tme π = path, a sequence of states -th state n π s π a kr = probablty of makng a transton from state k to state r a Pr( " = r " k ) kr =! = e k (b) = probablty that symbol b s emtted when n state k e ( b) = Pr( x = b! k ) k = BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 4 x = x, x2, x3 =,2, ()! (2)! (3)! = FFF = LLL = LFL () Pr( x,# ) = afef () affef (2) affef () =.5 " ".99 " ".99 "!.227 (2) Pr( x," ) = alel() allel(2) allel() =.5!.5!.8!.!.8!.5 =.8 (3) Pr( x,# ) = alel() alfef (2) aflel() al =.5 ".5 ".2 " ". ".5!.47 BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 42 BCB 444/544 Fall 7 Dobbs 7

8 # - Profles & HMMs 9/28/7 Identfyng the Most Probable Path The most lkely path π * satsfes: *! = argmax Pr( x,! )! To fnd π *, consder all possble ways the last "symbol" of x could have been emtted Let v ( ) = Prob. of path!, L,! most lkely Then k k to emt x, K, x such that! = k k r ( v ( a ) v ( ) = e ( x )max! ) r rk BCB 444/544 F7 ISU Dobbs # - Profles & HMMs 9/28/7 43 BCB 444/544 Fall 7 Dobbs 8