Two bioinformatics applications of dynamic Bayesian networks William Stafford Noble Department of Genome Sciences Department of Computer Science and Engineering University of Washington

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

The human genome in vivo Chromatin Fiber Gene ‘domains’ Nucleus Trans-factor complex DnaseI Hypersensitive Site Genes Genomic DNA Packaged into Chromatin

Measuring chromatin accessibility

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.

1.5 megabases

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.

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.

Spanning the gaps Beginning in State 1 (Insensitive)

Spanning the gaps Beginning in State 4 (Major DHS)

Selecting the number of states

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.

Capturing different scales

Enrichment of biologically relevant features

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.

Shotgun proteomics Training PSMs Test PSMs Trained Model Evaluation Probability Model PSM = peptide-spectrum match

Peptide sequence influences peak height

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%

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).

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?

Ion series modeled in a Markov chain

Vectors of log-odds ratios Correct peptide-spectrum matches Incorrect peptide-spectrum matches

Binary classifier

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%

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

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

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.

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