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**Two bioinformatics applications of dynamic Bayesian networks**

William Stafford Noble Department of Genome Sciences Department of Computer Science and Engineering University of Washington

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**Outline Segmenting genomic data Matching peptides to mass spectra**

Background: DNA, chromatin and DNase I Simple solution Wavelets Hierarchical model Matching peptides to mass spectra Background: tandem mass spectrometry Modeling peptide fragmentation

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**The human genome in vivo**

Chromatin Fiber Gene ‘domains’ Nucleus Trans-factor complex DnaseI Hypersensitive Site Genes Genomic DNA Packaged into Chromatin

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**Measuring chromatin accessibility**

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**A simple hidden Markov model**

very ^ Open chromatin Closed chromatin Each state contains a single Gaussian. The model has six parameters (two transitions, two means, two standard deviations). The parameters are initialized randomly and trained in an unsupervised fashion via expectation-maximization. EM is re-started 100 times, and we select the parameters that yield the highest likelihood. The original data set is then segmented using either Viterbi or posterior decoding.

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1.5 megabases

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**A problem, and two solutions**

Problem: We are interested in phenomena occurring at multiple scales. Solution #1: Perform a wavelet smooth prior to HMM analysis. Solution #2: Build a more complex probability model.

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**Change point model Four-state model:**

major DNase hypersensitive site (DHS), minor DHS, intermediate sensitivity region, and insensitive region. Continuous mixture of Gaussians at each state. Gamma distribution of lengths within each region.

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Spanning the gaps Beginning in State 1 (Insensitive)

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Spanning the gaps Beginning in State 4 (Major DHS)

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**Selecting the number of states**

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**Improved fit to the data**

Insensitive Intermediate sensitivity Minor DHS Major DHS Each panel is a QQ plot of the difference between the observed residuals and the theoretical Gaussian.

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**Capturing different scales**

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**Enrichment of biologically relevant features**

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**Future directions Many types of genomic data**

Phylogenetic conservation scores Various histone modifications Replication timing, etc. Perform segmentions in multiple dimensions simultaneously. Assign statistical significance to observed segments.

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**Shotgun proteomics Training PSMs Test PSMs Trained Model Evaluation**

Probability Model PSM = peptide-spectrum match

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**Peptide sequence influences peak height**

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Bayesian network We model peptide fragmentation using a Bayesian network. Nodes represent random variables, and edges represent conditional dependencies. Each node stores a conditional probability table (CPT) giving Pr(node|parents). Is b-ion observed? b-ion intensity 1.00 0.00 no b-ion observed 0.75 0.25 b-ion observed intensity > 50% intensity < 50%

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**Ion series modeled in a Markov chain**

Is b-ion observed? Is b-ion observed? Is b-ion observed? Is b-ion observed? Is b-ion observed? b-ion intensity b-ion intensity b-ion intensity b-ion intensity b-ion intensity ~ PepHMM (Han et al., 2005).

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**A more realistic model Is b-ion observed? b-ion intensity N-term AA**

C-term AA Is ion detectable? Fractional m/z Is proton mobile?

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**Ion series modeled in a Markov chain**

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**Vectors of log-odds ratios**

Correct peptide-spectrum matches Incorrect peptide-spectrum matches

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Binary classifier

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**Model Evaluation: Accuracy**

Training PSMs Test PSMs Trained Model Evaluation Probability Model Model Redundant TP/FP Unique TP/FP Bayes Net 285/300, 95% 137/144, 95.1% SEQUEST 288/300, 96% 136/144, 94.4% InsPecT 274/300, 91.3% 131/144, 90.9%

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**An incorrect identification**

Bayes net: HQDETQDALNALDLLTNEK SEQUEST: LRPGAELLEGAHVGNFVEMK This peptide does not appear in E. coli, the organism from which this protein sample was derived. Blue = b and y, green = a, red = ammonia loss, magenta = water loss, sienna = +2

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**Co-eluting peptides SEQUEST: AFPEAVLFIHPLDAK**

Bayes net: DVFVHFSALQGNQFK SEQUEST: AFPEAVLFIHPLDAK Blue = b and y, green = a, red = ammonia loss, magenta = water loss, sienna = +2

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Future directions Build a single Bayesian network that includes all ion types. Produce more descriptive outputs from the Bayesian network for input to the classifier. Add more biophysical details to the model: chromatography retention time, a better mass-to-charge estimate, etc. Generate a better (larger, more accurate) gold standard data set.

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**Acknowledgments DNase I hypersensitivity Wavelet analysis: Bob Thurman**

John Stamatoyannopoulos Pete Sabo Scott Kuehn many others in the Stam lab Wavelet analysis: Bob Thurman Change point model Charles Lawrence Heng Lian William Thompson Mass spectrometry Aaron Klammer Jeff Bilmes Sheila Reynolds Michael MacCoss

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