Jianlin Cheng, PhD. Department of Computer Science University of Missouri, Columbia. Fall, 2014
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1 Jianlin Cheng, PhD Department of Computer Science University of Missouri, Columbia Fall, 2014 Free for academic use. Jianlin Cheng & original sources for some materials
2 Find a set of sub-sequences of multiple sequences whose alignment has maximum alignment score (highest similarity). It is NP-hard. Biologically find highly conserved regions (motifs) of related genes or a protein family
3 GGAGCATAAA GGCGCATAAA GGAGTGTAAA GGTTTATAAG AGTGCATAAA
4 yeast: Gal4 drosophila mammal 1: actcgtcggggcgtacgtacgtaacgtacgtacggacaactgttgaccg 2: cggagcactgttgagcgacaagtacggagcactgttgagcggtacgtac 3: ccccgtaggcggcgcactctcgcccgggcgtacgtacgtaacgtacgta 4: agggcgcgtacgctaccgtcgacgtcgcgcgccgcactgctccgacgct Kathrina Kechris, 2005
5 Data: Upstream sequences from co-regulated/co-expressed genes. Assumption: Binding site occurs in most sequences 1: actcgtcggggcgtacgtacgtaacgtacgtacggacaactgttgaccg 2: cggagcactgttgagcgacaagtacggagcactgttgagcggtacgtac 3: ccccgtaggcggcgcactctcgcccgggcgtacgtacgtaacgtacgta 4: agggcgcgtacgctaccgtcgacgtcgcgcgccgcactgctccgacgct Goals: 1) Estimate motif 2) Predict motif locations 1: actcgtcggggcgtacgtacgtaacgtacgtacggacaactgttgaccg 2: cggagcactgttgagcgacaagtacggagcactgttgagcggtacgtac 3: ccccgtaggcggcgcactctcgcccgggcgtacgtacgtaacgtacgta 4: agggcgcgtacgctaccgtcgacgtcgcgcgccgcactgctccgacgct Kathrina Kechris, 2005
6 actcgtcggggcgtacgtacgtaacgtacgtacggacaactgttgaccg cggagcactgttgagcgacaagtacggagcactgttgagcggtacgtac ccccgtaggcggcgcactctcgcccgggcgtacgtacgtaacgtacgta agggcgcgtacgctaccgtcgacgtcgcgcgccgcactgctccgacgct Motif Size: 17 S = <a 1, a 2, a 3, a 4 > Construct a probability matrix (profile) A 1/4 1/4.... C 2/4 1/4 G 0 2/4 T 1/4 0
7 actcgtcggggcgtacgtacgtaacgtacgtacggacaactgttgaccg cggagcactgttgagcgacaagtacggagcactgttgagcggtacgtac ccccgtaggcggcgcactctcgcccgggcgtacgtacgtaacgtacgta agggcgcgtacgctaccgtcgacgtcgcgcgccgcactgctccgacgct A 1/4 1/4.... C 2/4 1/4 G 0 2/4 T 1/4 0 i Objective: Find the best position in each sequence that maximize product of probability Prob (posi_i) = 2/4 * 2/4 *.
8 actcgtcggggcgtacgtacgtaacgtacgtacggacaactgttgaccg cggagcactgttgagcgacaagtacggagcactgttgagcggtacgtac ccccgtaggcggcgcactctcgcccgggcgtacgtacgtaacgtacgta agggcgcgtacgctaccgtcgacgtcgcgcgccgcactgctccgacgct Construct a probability matrix (profile) from new positions A C 4/4 0 G 0 4/4 T 0 0
9 Don t know the motif model (probability matrix) Don t know the locations of each sub sequence
10 Dewey, 2013
11 Dewey, 2013
12 Dewey, 2013
13 Dewey, 2013
14 Objective: Design and develop a MCMC method to find a motif from a group of DNA sequence Other tools and data: ; Download the package to find the data in one of sub directories? MEME tool: Motif Visualization tool (weblogo):
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16 Assumption: size of motif is fixed Initialization: Make an initial guess of the motif locations and compute a probability matrix Repeat: Select one sequence randomly Calculate the motif probability matrix with the new position use all other sequences Use the matrix to evaluate the probabilities of all positions in the sequence (product of probability) Select (or sample) a position in the sequence according to their probability Until matrix converges or other criterion.
17 Sample a position according to probability i actcgtcggggcgtacgtacgtaacgtacgtacggacaactgttgaccg cggagcactgttgagcgacaagtacggagcactgttgagcggtacgtac ccccgtaggcggcgcactctcgcccgggcgtacgtacgtaacgtacgta agggcgcgtacgctaccgtcgacgtcgcgcgccgcactgctccgacgct A 1/4 1/4.... C 2/4 1/4 G 0 2/4 T 1/4 0 Compute P i = 2/4 * 2/4 *. 1<=i<=n) Select a position according to its Normalized probability. Sample probability of i = n p i= 1 i p i
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23 Output of Gibbs Sampler Prob Matrix actcgtcggggcgtacgtacgtaacgtacgtacggacaactgttgaccg cggagcactgttgagcgacaagtacggagcactgttgagcggtacgtac ccccgtaggcggcgcactctcgcccgggcgtacgtacgtaacgtacgta agggcgcgtacgctaccgtcgacgtcgcgcgccgcactgctccgacgct Confidence Start pos Motif End pos
24 Logos Graphical representation of nucleotide base (or amino acid) conservation in a motif (or alignment) Information theory 2 + pb ( )log 2 pb ( ) b= { A,C,G,T } Height of letters represents relative frequency of nucleotide bases Kathrina Kechris, 2005
25 Visualization goals (1) The height of the position is proportional to the information contained at the position (2) The height of a letter is proportional to the probability of the letter appearing at the position Two new concepts related to probability matrix: Entropy Information
26 Entropy is a measure of uncertainty of a distribution i pi log2 p i A C G T 1/4 1/4 1/4 1/ /2 1/2 0 0 What is the entropy Of positions 1,2,3?
27 Information is the opposite of entropy. It measures the certainty of a distribution Information = maximum entropy the entropy of a position (or distribution) Maximum entropy for n characters is the Entropy when n characters are uniformly Distributed. log 2 n Info. Of pos 1= 2 2 = 0 Info. Of pos 2 = 2 0 = 2 Info. Of pos 3 = 2-1 = 1
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29 Develop your Gibbs sampling program to find motifs in a group of gene sequences Test the program on a number of sequence groups Analyze the algorithm, program and results (speed, robustness, accuracy, quality, visualization, comparison, alternative solutions)
30 Group 1: Jie Hou, Minguan Song, Tuan Trieu, Meng Zhang, Hao Sun Group 2: Abhishek Shah, Mike Phinney, Chao Fang, Ma< England Group 3: Xinjian Yao, Yuxiang Zhang, Rui Xie, Muxi Chen, Xinwei Du Group 4: Kevin Melkowski, Michael Pieper, Mary Sheahen, Kristofferson Culmer Others: parocipaong in discussion
31 Group Discussion Problem definition Algorithm Implementation Evaluation Visualization Task Assignment Select Coordinator Data Sharing Communication Brief Introduction by Deb (5 10 minutes) Discussion of Plan (40) Informal Presentation on whiteboard (5-6 minutes per group)
32 Make an official plan in PPT Present your plan by coordinator: 15 minutes presentation + 3 minutes question-answer Create your data sharing account on public cloud Send your revised plan to mumachinelearning@gmail.com after presentation Present your results on Sept. 19 (Friday)
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