Modeling Motifs Collecting Data (Measuring and Modeling Specificity of Protein-DNA Interactions)

Transcription

1 Modeling Motifs Collecting Data (Measuring and Modeling Specificity of Protein-DNA Interactions) Computational Genomics Course Cold Spring Harbor Labs Oct 31, 2016 Gary D. Stormo Department of Genetics Outline Modeling specificity with a position weight matrix (PWM) General features Limitations and extensions How to set the weights General ideas, some history Using high-throughput experimental data Using in vivo location data (Chip-chip/seq) 1

2 {Sites} Terminology: Sites vs Motifs Motif Think restriction sites EcoRI: {GAATTC} GAATTC HincII {GTTAAC,GTTGAC,GTCAAC,GTCGAC} GTYRAC Transcription factor motifs should be quantitative, give different scores to different sites, reflecting differences in binding affinity Also: site is specific location in genome Representations/Models of Protein-DNA binding Transcription factors don t bind to just one sequence A Consensus sequence is usually the preferred site, but similar sequences also bind well Not all variants bind equally well; some positions contribute more to the specificity than others 2

3 Position Weight Matrix Model (PWM, also PSSM) A: C: G: T: PWM Model Score = -24.A C T A T A A T G T A: C: G: T:

4 PWM Model Score = 43.A C T A T A A T G T A: C: G: T: A: C: G: T:

5 PWM Model A: C: G: T: PWM is a generalization of consensus sequence. There is NO advantage in consensus sequences. Given a consensus sequence one can define a PWM and a threshold that will return the same sites. PWM Model A: C: G: T: Score( S ) W S i PWM is a linear model: S i encodes the sequence (which base occurs at each position) W weights those encoded features to provide the score Easy to add more features if they are necessary i 5

6 Two important issues need to be addressed Parameter estimation: Where do the matrix elements come from? Different types of data lead to different methods of parameter estimation. Additivity: do the positions really contribute independently to the binding interaction? If not, how to we extend the model? Complete binding energy list vs model. 6

7 If simple additive model is inadequate, can use di-nucleotide or higher-order models. Some form of a matrix model must be correct because binding the binding data itself is a matrix (vector) AA AC AG AT TT AAA AAC AAG AAT TTT Alternative approach to higher-order contributions: structure parameters Maybe the non-additivity is due to structural preferences known to be dependent on nearest neighbor bases (or longer) May capture context effects with fewer parameters For example, see work by Rohs and colleagues: Covariation between homeodomain transcription factors and the shape of their DNA binding sites. Nucleic Acids Res : TFBSshape: a motif database for DNA shape features of transcription factor binding sites. Nucleic Acids Res (Database issue):d Quantitative modeling of transcription factor binding specificities using DNA shape. Proc Natl Acad Sci U S A (15): DNA Shape Features Improve Transcription Factor Binding Site Predictions In Vivo. Cell Syst Sep 28;3(3):

8 How to Set the Matrix Elements Statistical treatment of known sites. Need a reasonable sample size. Some assumptions about how the sample is obtained. - probabilistic model is easy, can be accurate if assumptions are reasonable Quantitative binding data: determine matrix parameters that provide the best fit. - Has been laborious and slow experimental work, but new technologies make this much easier Modeling based on known sites N(b,i) PFM or PPM Note: some papers and programs call this a PWM Log-odds PWM F(b,i) W(b,i) = log[f(b,i)/p(b)] I(i) = F(b,i)W(b,i) 8

9 Classic Logo (from Tom Schneider): Height of column at each position is Information Content Each base in proportion to its frequency Likelihood Ratio Statistics Primer Given two probability distributions P i and Q I P i = Q i = 1 And some data, D i, which is number of times each type i is observed in N total observations The Likelihood Ratio of the data being from distribution Q i versus P i is: LR = (Q i /P i ) Di And the log-likelihood Ratio is LLR = D i ln (Q i /P i ) 9

10 LLR = D i ln (Q i /P i ) Maximum likelihood distribution is Q i = D i /N So max LLR = N Q i ln (Q i /P i ) Q i ln (Q i /P i ) 0 Information Content Relative Entropy Kullbach-Liebler Distance Related to G-statistic and χ 2 Modeling from experimental data From single binding site experiments to highthroughput methods that allow for the determination of specificity (relative affinity) across all possible sequences at once 10

11 Quantitative Binding Affinity of TF for one sequence Specificity Refers to the relative Affinity to different Sequences, ideally to All sequences 11

12 High-throughput experimental methods to Measure TF specificity Specificity Modeling High-throughput in vitro binding site analyses Can give good, quantitative models of intrinsic binding specificity More data alone isn t sufficient to give better models, also need good analysis methods Log-odds method is based on assumptions that may not be true Energetic models can give better descriptions Non-linear relationship between binding affinity and binding probability at high TF concentration 12

13 Log-odds method is equivalent to an energy model if the sites are from a Boltzmann distribution with binding probability e E posterior prior energy E F( S ) P( S ) e i / Z i i E i FS ( i ) ln PS ( ) i Log-odds relationship between binding energy and frequencies Reality is a Fermi-Dirac distribution with Boltzmann a special case at the low concentration range Djordjevic et al, Genome Res :

14 GTGGA vs ATGGA E G -E A =2kT GTGTA vs ATGTA Additive changes in binding energy have non-independent (context dependent) effects on binding probability Probabilities no longer factor, even though energies are additive HT-SELEX (SELEX-Seq) min [ N( S ) n( S )] i a N( Si) b n( Si) data WS i 1 e Parameters to fit: a, b, W, μ i i 2 14

15 Fit of model to HT-SELEX data for zif268 BEEML vs BioProspector Zhao et al, PLoS Comp Bio, 2009 Protein Binding Microarray (PBM) 15

16 Example of Plag1 using BEEML-PBM Zhao and Stormo, Nature Biotechnol : Nat Biotechnol : Most TFs (~90%) fit well by PWMs BEEML-PBM among the best methods Some do better with di-nucmodels A few require multiple modes of interaction Best models fit in vivo data as well as in vivo-derived models 16

17 Diverse sets: >100 TFs ~20 TFs ~240 TFs Weirauch et al >1000 TFs Bacterial-1-Hybrid (B1H) 17

18 B1H on zif268 returns the expected model 18

19 Average Prediction Accuracy for ZFPs HT-SELEX (SELEX-Seq) P(S i b) P(S i ) 1 1+e E i μ Compared to reference sequence with E = 0 P S i b P S i P S ref b = P S ref 1+e μ 1+e E i μ 19

20 Spec-seq (specificity by sequencing) P(S i b) P(S i u) = eμ E i Compared to reference sequence with E = 0 P S ref b P S ref P S i b = e E i ln P S i P S ref b P S ref P S i b P S i = E i Spec-seq: Specificity by sequencing P + S i P S i K A (S i ) = [P S i] P [S i ] K A S 1 : K A S 2 : : K A S n = P S 1 S 1 : P S 2 S 2 : : P S n S n 20

21 Specificity of the Lac repressor WT operator is asymmetric 4 libraries: vary both sequence and spacing 2560 different binding sites Highly reproducible: ~5% variance in affinity ~0.1kT variance in energy Zuo and Stormo, Genetics, 2014 Three dimensional structure of the dimeric lac HP62 O1 operator complex. Kalodimos C G et al. EMBO J. 2002;21: by European Molecular Biology Organization 21

22 No motif for half of all human TFs Most are C2H2 zinc finger proteins Laura Campitelli No motif for half of all human TFs Most are C2H2 zinc finger proteins No motif (809) Known motif (637) Close ortholog/paralog has motif (219) Human all TFs (1,665) Not tried/ no data (37) C2H2 with No motif (573) Human no motif (809) Needs heterodimerization partner (56) Possibly not sequencespecific (143) No motif (573) Human all C2H2s (714) Known motif Close (97) ortholog/par alog has motif (44) Matt Weirauch 22

23 ZF specificity prediction Use three programs: ours, One from Princeton group, One from Toronto group The Logos look pretty different but that is largely quantitative, and there are many high IC positions of agreement. By averaging the PFMs one can obtain a consensus sequence that agrees pretty well with all three. Spec-seq randomizations: Reverse Consensus (30bp) TCTTGATGATGCTGCAATATTAATAATTTA Consensus is good enough to show shift in EMSA. So we randomized five adjacent positions at a time, generating 6 libraries of 1024 sequences. Merged Logo shows overall good match with consensus and provides quantitative predictions about binding energy contributions. 23

24 Spec-seq motif matches well with motif obtained from in vivo recombination hotspots and using Affinity-seq method Affinity-seq pulls out genomic DNA fragments in vitro and sequences them without Amplification. Affinity-seq motif Hotspot motif Can also be easily adapted to study CpG methylation sensitivity ZFP57 involved in Imprinting Maintenance Has 2 ZF clusters, one binds TGCCGC, prefers mcpg 3 libraries with random regions and methylation variants 24

25 Spec-seq for combinatorial binding can get all of the important parameters in one experiment, including cooperativity K X x 1 : K X x 2 : : K X x n = N x 1 B X, N x 1 B, : N x 2 B X, N x 2 B, : : N(x n B X, ) N(x n B, ) K X Y x 1 : K X Y x 2 : : K X Y x n = N x 1 B X,Y N x 1 B,Y : N x 2 B X,Y N x 2 B,Y : : N(x n B X,Y ) N(x n B,Y ) ω i = K X Y S i K X S i = K Y X S i K Y S i = K X,Y S i K X S i K Y S i Stormo, Zuo, Chang, Briefings in Functional Genomics, 2015 Conclusions: 1. Different types of high-throughput data can be used to obtain good specificity models; good analysis methods are critical 2. PWMs are often (usually?) good approximations, but higher order models can be obtained if needed Specificity Modeling 25

26 Discovery of Binding Motifs from in vivo data Datatypes for Motif Discovery Co-regulated genes Genetic studies (deletion, over-expression effects) Expression analysis (microarrays, RNA-Seq) Co-bound regions ChIP-chip/-Seq location analysis Phylogenetic analysis, conservation across species phylogenetic footprinting Can be combined with multigene analysis, even over the whole genome Goal: Find the most significant pattern in common Can t look at all possible alignments too many In vitro analysis methods don t work; assumptions not valid Outline of problem 26

27 Example dataset: promoter region from co-regulated genes CE1CG \TAATGTTTGTGCTGGTTTTTGTGGCATCGGGCGAGAATAGCGCGTGGTGTGAAAGACTGTTTTTTTGATCGTTTTCACAAAAATGGAAGTCCACAGTCTTGACAG\ ECOARABOP \GACAAAAACGCGTAACAAAAGTGTCTATAATCACGGCAGAAAAGTCCACATTGATTATTTGCACGGCGTCACACTTTGCTATGCCATAGCATTTTTATCCATAAG\ ECOBGLR1 \ACAAATCCCAATAACTTAATTATTGGGATTTGTTATATATAACTTTATAAATTCCTAAAATTACACAAAGTTAATAACTGTGAGCATGGTCATATTTTTATCAAT\ ECOCRP \CACAAAGCGAAAGCTATGCTAAAACAGTCAGGATGCTACAGTAATACATTGATGTACTGCATGTATGCAAAGGACGTCACATTACCGTGCAGTACAGTTGATAGC\ ECOCYA \ACGGTGCTACACTTGTATGTAGCGCATCTTTCTTTACGGTCAATCAGCAAGGTGTTAAATTGATCACGTTTTAGACCATTTTTTCGTCGTGAAACTAAAAAAACC\ ECODEOP2 \AGTGAATTATTTGAACCAGATCGCATTACAGTGATGCAAACTTGTAAGTAGATTTCCTTAATTGTGATGTGTATCGAAGTGTGTTGCGGAGTAGATGTTAGAATA\ ECOGALE \GCGCATAAAAAACGGCTAAATTCTTGTGTAAACGATTCCACTAATTTATTCCATGTCACACTTTTCGCATCTTTGTTATGCTATGGTTATTTCATACCATAAGCC\ ECOILVBPR \GCTCCGGCGGGGTTTTTTGTTATCTGCAATTCAGTACAAAACGTGATCAACCCCTCAATTTTCCCTTTGCTGAAAAATTTTCCATTGTCTCCCCTGTAAAGCTGT\ ECOLAC \AACGCAATTAATGTGAGTTAGCTCACTCATTAGGCACCCCAGGCTTTACACTTTATGCTTCCGGCTCGTATGTTGTGTGGAATTGTGAGCGGATAACAATTTCAC\ ECOMALBA \ACATTACCGCCAATTCTGTAACAGAGATCACACAAAGCGACGGTGGGGCGTAGGGGCAAGGAGGATGGAAAGAGGTTGCCGTATAAAGAAACTAGAGTCCGTTTA\ ECOMALBA \GGAGGAGGCGGGAGGATGAGAACACGGCTTCTGTGAACTAAACCGAGGTCATGTAAGGAATTTCGTGATGTTGCTTGCAAAAATCGTGGCGATTTTATGTGCGCA\ ECOMALT \GATCAGCGTCGTTTTAGGTGAGTTGTTAATAAAGATTTGGAATTGTGACACAGTGCAAATTCAGACACATAAAAAAACGTCATCGCTTGCATTAGAAAGGTTTCT\ ECOOMPA \GCTGACAAAAAAGATTAAACATACCTTATACAAGACTTTTTTTTCATATGCCTGACGGAGTTCACACTTGTAAGTTTTCAACTACGTTGTAGACTTTACATCGCC\ ECOTNAA \TTTTTTAAACATTAAAATTCTTACGTAATTTATAATCTTTAAAAAAAGCATTTAATATTGCTCCCCGAACGATTGTGATTCGATTCACATTTAAACAATTTCAGA\ ECOUXU1 \CCCATGAGAGTGAAATTGTTGTGATGTGGTTAACCCAATTAGAATTCGGGATTGACATGTCTTACCAAAAGGTAGAACTTATACGCCATCTCATCCGATGCAAGC\ PBR322 \CTGGCTTAACTATGCGGCATCAGAGCAGATTGTACTGAGAGTGCACCATATGCGGTGTGAAATACCGCACAGATGCGTAAGGAGAAAATACCGCATCAGGCGCTC\ TRN9CAT \CTGTGACGGAAGATCACTTCGCAGAATAAATAAATCCTGGTGTCCCTGTTGATACCGGGAAGCCCTGGGCCAACTTTTGGCGAAAATGAGACGTTGATCGGCACG\ TDC \GATTTTTATACTTTAACTTGTTGATATTTAAAGGTATTTAATTGTAATAACGATACTCTGGAAAGTATTGAAAGTTAATTTGTGAGTGGTCGCACATATCCTGTT\ 27

28 Expectation Maximization (EM) Approach to Motif Discovery Basic Idea: - Given sites, estimate PWM (log-odds model) - Given PWM, pick likely sites according to their probability - Make initial guess, then iterate between those steps until convergence Algorithm: Initial PWM from average of all possible sites Using current PWM estimate probability of each position being site; make new PWM from weighted average of all sites Iterate to convergence; usually fast, no guarantee of optimal Gibbs Sampling Approach to Motif Discovery Same Basic Idea: - Given sites, estimate PWM (log-odds model) - Given PWM, pick likely sites according to their probability - Iterate between those steps until convergence Algorithm: Pick 1 site from N-1 sequences, make PWM Use pseudocounts to avoid prob. = 0 Use current PWM to pick site from left out sequence by sampling from probability disturbition; update PWM Iterate to convergence; run multiple times, compare results; still no guarantee of optimal but avoids local optima often obtained with EM 28

29 From Lawrence et al, (1993) Science 1 262: Motif discovery from co-regulated genes Single species Multiple species A B 29

30 Alignment of conserved regions Alignment of profiles Example Leu3 YGL125W S. cerevisiae GAAAAAATAACAGCGACTTTTCTCCCGGTAGCGGGCCGTCGTTTAGTCATTCTATCCCTC S. mikatae AAAACATAACAGCGAATTTTCCTCCCGGTAGCGGGCCTTCGTTTAGTCATTCTCTCTCTT S. bayanus AAAAAATAACAGCGACTTTTCCCCCCGGTAGCGGGCCGTCGTTTAGTCATTCTCTCTCCC S. kudriavzevii GAAAAAAAACAACGGCGGCCTCCCCCGGTAGCGGGCCGTCGTTTAGTCATTCTCTCTCTC ***** **** ** *** * ************************************* YOR108W S. cerevisiae GCCATCATGGTCCGGTAACGGTCGTAGTGAATGACTCATATTTTTCCATCTCTTT S. mikatae GCCATCAAGGTCCGGTAACGGTCGTAGTGAATGACTCACATTTTCTTCGTTATTC S. bayanus ACCATTACGGTCCGGTAACGGACTTAGTGAATGATTCATCTTTTCTTCTTTTTTC S. kudriavzevii GTCGTTAAGGTCCGGTAACGGCCCTCAGCGAATGATTCATAATTTCATTTTTTTC ***** * ************* * ********** *** **** *** *** YMR108W S. cerevisiae AACGCCTAGCCGCCGGAGCCTGCCGGTACCGGCTTGGCTTCAGTTGCTGATCTCGG S. mikatae CACAATGACACATACCTAACAGCCGGTACCGGCTTGAATGCCGCCGTTGGCTTCGG S. bayanus ATCTTCTAGTCACCGCAGTCTGCCGGTACCGGCTTGAATTCCGCCGTTGATCCTGG S. kudriavzevii CACATCTCTAGTCCGCGCTCTGCCGGTACCGGCTTAGACTAGCCACGAATCTCGGC ** *** * **** ***************** **** ** * ** ** YGL125W YOR108W YMR108W A C G T A C G T A C G T Wang and Stormo, Bioinformatics 2003 Even whole genome search for conserved, multi-copy elements (eg. PhyloNet) Wang and Stormo, PNAS