Bio informatics, Sequence tags, log odds and profile
- 1. Bioinformatics 1 -- lecture 10 Sequence weights log-odds profiles Logos
- 2. Modeling a sequence family In statistical modeling, we choose we build a representative model for the sequence family. To choose the representative, we take a poll over all observed sequences. Are they a representative sample? family sequence space superfamily
- 3. A typical poll of the database If we submit one sequence (for example, citrate synthase from human) to the GenBank database (using BLAST for example), and take 100 results, and we build a cladogram from this, we might get something like this... primates rabbit rat E. coli lawyer What is our representative going to look like if we use the rule: "one sequence one vote"?
- 4. Sequence weighting corrects for poor sampling To build a representative model we can... (1) throw out all redundant sequences and keep representatives of each clade only, or (2) apply a weight to each sequence reflecting how non- redundant that sequence is. One measure of non-redundancy is sequence-distance, or evolutionary distance.
- 5. Crude weights from a cladogram Simplest weighting scheme: Start with weight = 1.0 at the common ancestor of the tree. Split the weight evenly at each node. primates rabbit rat E. coli lawyer 1.000 0.500 0.500 0.250 0.250 0.125 0.125 0.0625 0.0625 0.008 0.0625 0.125 0.125 0.0625 0.016 0.016 0.016 0.016 0.016 0.008 0.008 0.016 0.008 0.031 0.031 0.031 0.031 0.0625 Human sequences are 10/18 of the tree, but only 0.125 of the weights
- 6. Better weights from a phylogram 0.5 0.3 0.1 0.2 The sequence weight is calculated starting from the distance from the taxon to the first ancestor node, adding half of the distance from the first ancestor to the second ancestor, 1/4th of the distance from the second to third ancetor, and so on. Finally, the weights are normalized. A B C wA = 0.2 + 0.3/2 = 0.35 wB = 0.1 + 0.3/2 = 0.25 wC = 0.5
- 7. Making a phylogram in Geneious • Align • Make tree • turn off “transform branches” – Resulting branches are proportional to p- distance 7
- 8. (Easy) Distance-based weights Self-consistent Weights Method of Sander & Schneider, 1994 0.3 1.0 0.9 A B C C B A all wi initialized to 1. while (wi ≠ w'i) do for i from A to C do w'i = Σj wj Dij end do for i from A to C do wi = w'i/ Σj w'j end do end do (1) Sum the weighted distances to get new weights. (2) Normalize the new weights (3) Repeat (1) and (2) until no change. Pseudocode :
- 9. Distance-based weights 0.3 1.0 0.9 A B C C B A w'A = 0.3 + 1.0 = 1.3 w'B = 0.3 + 0.9 = 1.2 w'C = 1.0 + 0.9 = 1.9 wA = 1.3/(1.3+1.2+1.9)=0.30 wB = 1.2/4.4 = 0.27 wC = 1.9/4.4 = 0.43 w'A= 0.3*0.27+1.0*0.43=0.51 w'B= 0.3*0.3+0.9*0.43 =0.48 w'C= 1.0*0.3+0.9*0.27 =0.54 ... wABC = 0.33 0.31 0.35 wABC = 0.30 0.28 0.42 wABC = 0.31 0.29 0.40 wABC = 0.30 0.28 0.41 wABC = 0.30 0.28 0.41 converged. (3) Repeat (1) and (2) until no change. Running the pseudocode : (1) Sum the weighted distances to get new weights. (2) Normalize the new weights (1) Sum the weighted distances to get new weights.
- 10. Amino acid probability profiles An amino acid profile is defined as a set of probability distributions over the 20 amino acids, one PDF for each position in the alignment. Gap probabilities may or may not be included when talking about a profile. A C D E F G H I K L M N P Q R S T V W Y Amino acids are not equally likely in Nature. K, L and R are the most common.
- 11. Profile 11
- 12. Usually, Log-likelihood ratios LLR(a) = log( P(a|i) / P(a) ) probability of a in one column likelihood of a overall (the whole database)
- 13. Pseudocounts, because you never know... LLR(a) = log( P(a|i) / P(a) ) If P(a|i)=0., you can't take the log The probability of seeing a in column i of a sequence alignment is never really zero. So we add a small number of 'pseudocounts' ε. LLR(a) = log( P(a|i)+ε / P(a) ) This LLR does not go to negative infinity as P(a)-->0.000. Instead it goes to log(ε/P(a)).
- 14. Color = LLR. Blue = high negative values. Green = zero. Red = high positive values. Color matrix One way to visualize profiles
- 15. Another way: Logos Height of letter is the LLR.
- 16. Example Logos for DNA alignments
- 17. Alignments of transcription factor footprint sites
- 18. Scoring a sequence versus a profile KEMGFDHIIIHP score = Σi LLR(ai) The score is the sum of the log- likelihood ratios of the amino acid in the sequence. Sequence=
- 19. In class exercise: build a profile Copy “tree of 5” from Collaboration-->Bioinformatics1@RPI Display as a phylogram On paper... (1) Calculate sequence weights based on the distances, using one iteration of distance-based weights. wA = Σi DiA Then normalize (divide by Σi wi ). (2) Sum the probabilities of each AA in the nth column. i.e. P(A) = sum wi over sequences that contain an A. (3) Convert each P() to a LLR using equal probability AAs (0.05) as the expected value. Use a pseudocount of 0.02 LLR = log((P(n)+0.02)/(0.05)) (4) Divide by log(2) to convert to 'bits'. (5) Stack letters, Logo style. Height of letter = bits.
- 20. Aligning sequence to profile S(i,j) = 0 do aa=1,20 S(i,j) = S(i,j) + P(aa,i)*B(aa,s(j)) enddo 20 Aligning profile to profile S(i,j) = 0 do aai=1,20 do aaj=1,20 S(i,j) = S(i,j) + P(aai,i)*P(aaj,j)*B(aai,aaj) enddo enddo profile1@i P(aa|i) BLOSUM score No need to normalize, since ∑ ∑ P(aai|i)*P(aaj|j)= 1 sequence2@j aai aaj
- 21. Psi-BLAST: Blast with profiles Psi-BLAST searches the database iteratively. (Cycle 1) Normal BLAST (with gaps) (Cycle 2) (a) Construct a profile from the results of Cycle 1. (b) Search the database using the profile. (Cycle 3) (a) Construct a profile from the results of Cycle 2. (b) Search the database using the profile. And So On... (user sets the number of cycles) Psi-BLAST is much more sensitive than BLAST. Also more vulnerable to low-complexity.
- 22. Other forms of BLAST 22 BLAST query database blastn nucleotide nucleotide blastp protein protein tblastn protein translated DNA blastx translated DNA protein tblastx translated DNA translated DNA psi-blast protein, profile protein phi-blast pattern protein transitive blast* any any *not really a blast. Just a way of using blast.
- 23. PHI-BLAST -- Patterned Hit Initiated BLAST 23