1. Evaluation of count scores for weight matrix motifs Project Presentation for CS598SS Hong Cheng and Qiaozhu Mei

2. Problem Background • Understand the mechanism of gene regulation and predict the gene regulation. • Need a quantitative measure of the strength of a TF Binding Site correlated in a gene sequence. • This measure can be used as an important feature in the study of gene regulation.

3. Project Background (cont.) • There are no standard criteria for such a measure. • But we expect a good measure can model • The quality of a Binding Site. • The occurrence of a binding site in the sequence. • There can be many choices for such a measure, but which one is better…?

4. Project Overview • Project Goal • Possible scoring measures • Evaluate a score: Constraint Analysis • Experiments and results • Current Status and Future Work

5. Goal of the project • Three Steps: • Formalize the problem of counting score of weight matrix motifs and propose an evaluation mechanism. • Evaluate the existing scoring methods of weight matrix motifs. • Either suggest a good motif counting method or propose a new score better than existing scores.

6. Possible scoring measures • Simple Counting • Match or not match • Likelihood Sum • Data likelihood of a site is generated by a motif: sum over all possible sites • Model based scores • Free Energy • Normalization of existing scores

7. Simple counting • Simple Counting (match or not match) • Doesn’t work for fuzzy motifs • Variation: count a motif if for a subsequence, P(s|w) is above a threshold. • Likelihood sum score • A soft version of simple counting • Ad hoc, doesn’t have a sound probabilistic interpretation

8. Model Based Scores • Consider the sequence to be generated by a model involving a set of motifs • HMM model: Stubb (Sinha et al 2003) • Count of a motif as an average number of times the motif is planted in the sequence • Two options: • With fixed transition probabilities • Fitting transition probabilities by unsupervised learning

9. Other Possible Scores • Free Energy: • : a set of motifs M and model parameters • b: model parameters and only backgrounds • F(s, ) = log( Pr(S| )/ Pr(S| )) • Models the score of a sequence and a set of motifs, cannot give score of a specific motif unless run the computation for only one motif • Normalization of Existing Scores • Estimating P(C >= x) instead of #sequences • Use well known normalization methods to normalize the actual counts • Min-Max; Z-Score ( Z = (N-E)/S)

10. Question:What makes a good score for weight matrix motif?

11. Evaluation of scores • Empirical evaluation with Lab Experiments • Comparing the score with lab experiments to see the effectiveness • ChIP to Chip studies • Problem: • Lab experiment data not easy to get • Performance may vary over species (thus may be biased) • Analytical evaluation: heuristic constraints

12. Analytical Evaluation with Heuristic Constrains • There are many heuristic constraints which we expect a good score will satisfy • The effectiveness of a score can be implied by how good it satisfies the constraints • Whether a score satisfy a constraint can be studied analytically or with experiments on random data • Combining with empirical evaluation, constraint analysis can tell us why a score is better than others, and help us defining a new score.

13. Heuristic Constraints (I) • Formalization • Motif PWMs: w, M • Sequences: S • Possible binding sites: s • Score of the nth run: Cn(S, w) • Motif Quality Constraint • Focus on quality of sites • Contribution of a motif w with length l on sites • For one motif w, two sequence S1, S2, a site position [i , i + l - 1]. S1[i , i + l - 1] != S2[i , i + l - 1] and other positions are the same. • If I(S1[i , i + l - 1] ) <= I(S2[i , i + l - 1] ) • C(S1, w) >= C(S2, w)

14. Heuristic Constraints (II) • Motif Length Constraint • For two motifs w1 and w2, length(w1) = length(w2) + 1. For any position i <= length(w2), the multinomial vector w1(i) = w2(i) . • Compute the score of M1 and M2 on one sequence S independently • C(S, w1)<= C(S, w2) • Motif Sharpness Constraint • For two motifs w1 and w2, length(w1) = length(w2), if for any position i, j = 0, 1, 2, w1(i, j) < w2(i, j) and w1(i, 3) > w2(i, 3) • (w1 is sharper than w2) • Compute the score of w1 and w2 on a large number of sequences independently • Expectation [C(w1)]<= Expectation [C(w2)]

15. Heuristic Constraints (III) • Motif Probability Constraint • For one motif w, one sequence S, if we compute the score C(S, w) two times and give higher probability to w in the second run • (e.g. transition probability or prior probability in HMM) • E.g. p1< p2 • C1(S, w) <= C2(S, w) • Motif Competition Constraint • For two motifs w1 and w2, one sequence S. First compute the score for w1 only, then compute considering the co-occurrences of w1 and w2. • C1(S, w1) >= C2(S, w2)

16. Heuristic Constraints (IV) • Deterministic Constraint • One motif w, one sequence S, if we compute the score of w twice with no parameter changing, • C1(S, w) = C2(S, w) • Upper Bound Constraint • An existing set of motifs M, a sequence S. if we adding a new motif wn and compute the scores for M and wn again, • But cannot exceed an upper bound (e.g. the length of S)

17. A summary of constraints • The heuristic constraints can allow us to analyze the effectiveness of a score without doing experiments. • In experiments show that one score is better than others, the heuristic constraints can indicate why it is better. • Difficult to find a close set of constraints • Some constraints are closely related (maybe not orthogonal, though not redundant)

18. Experiment Design • Regular (comparing distribution): • Method • Stubb with learnt p • Simple Count • Data • Real motifs, real sequence data • Real motifs, random generated very long sequence (say, 10k~100k) • Random motifs, including long, short, fuzzy and sharp combinations, random long sequence

19. Experiment Design • Stubb with Fixed Prior Probability • Vary prior prob p : 0.0001, …, 0.001, …, 0.01… • Data • Real motifs, random generated long sequence • Random motifs, including long, short, fuzzy and sharp combinations, random generated long sequence • See score distribution

20. Experiment Design: Constraints • Motif Length: • Random generated motifs (uniform, varying length), random generated long sequence. • Random generated motifs (uniform, varying length), real sequences • Motif sharpness: • Random generated motifs (varying sharpness, equal length), random generated long sequence (100k)

21. Experiment Design: Constraints • Motif Competition • Real motifs, real sequence/random sequence data • several runs: • 1st run: only motif M1 • 2nd run: M1 and M2, • 3rd run: M1 and M2 and M3, • … • Plot the distribution of M1 in several runs.

22. Experiment Design (cont.) • Deterministic constraints: • Real motifs, real sequences, run it several times, plot the distributions of Motif 1 to see whether it changes a lot. • Normalization: • Z-Score only; Min-Max only; P(C>=N) only; P(C>=N) + Z-Score; P(C>=N) + Min-Max

23. Experiment Result(1) • Stubb on real sequences against real motifs • Simple count on real sequences against real motifs • Four motifs • Bicoid, length 11, medium sharp • Kruppel, length 9, medium sharp • Gt, length 12, a bit sharper • Hkb, length 7, sharpest, every row has one non-zero count and three 0s

24. Experiment Result (1)-Stubb

25. Experiment Result (1)-Simple Count

26. Experiment Result (1) – Normalization P(x>=N)

27. Result (1) – Normalization z-score on motif score

28. Experiment Result(2) • Stubb on random sequences against random motifs • Simple count on random sequences against random motifs • Four motifs • Long_fuzzy, length 20, uniform • Long_sharp, length 20, sharp • Short_fuzzy, length 5, uniform • Short_sharp, length 5, sharp

29. Experiment Result(2)-Stubb

30. Experiment Result (2)-Simple Count

31. Experiment Result(3) • Stubb with Fixed Prior Probability, varying p 0.0001 ~0.05 • Four real motifs • Bicoid • Kruppel • Hkb • Gt • Four random motifs • Long_fuzzy • Long_sharp • Short_sharp • Short_fuzzy

32. Experiment Result(3)-Bicoid

33. Experiment Result(3)-Hkb

34. Experiment Result(3)-Long_fuzzy

35. Experiment Result(3)-Short_sharp

36. Experiment Result(4)-Constraint Motif Length • Test on this heuristic • Stubb • Simple Count • Generate 10 random motifs, uniform, vary length from 1 to 10

37. Experiment Result(4)-Stubb

38. Experiment Result(4)-Simple count

39. Experiment Result(5)-Contraint Motif Sharpness • Test on this heuristic • Stubb • Simple Count • Generate 10 random motifs, length 10, vary sharpness

40. Experiment Result(5)-Stubb

41. Experiment Result(5)-Simple count

42. Experiment Result(6)-Motif Competition • Test on this constraint • Stubb • Simple Count • 1st run: using bicoid only • 2nd run: using bicoid and other five motifs • 3rd run: using bicoid and other nine motifs • Monitor the bicoid score

43. Experiment Result(6)-Stubb

44. Experiment Result(6)-Simple count

45. Summary

46. Future Work • Finish constraint tests • Evaluate more scores (e.g. Free Energy) • Define and formalize more constraints • Comparing with ChIP-chip experiment results, study the effectiveness of scores and the relation to constraints