L14

1. L14 Mass Spec Quantitation MS applications Microarray analysis CSE182

2. Biol. Data analysis: Review Assembly Protein Sequence Analysis Sequence Analysis/ DNA signals Gene Finding CSE182

3. Other static analysis is possible Genomic Analysis/ Pop. Genetics Assembly Protein Sequence Analysis Sequence Analysis Gene Finding ncRNA CSE182

4. A Static picture of the cell is insufficient • Each Cell is continuously active, • Genes are being transcribed into RNA • RNA is translated into proteins • Proteins are PT modified and transported • Proteins perform various cellular functions • Can we probe the Cell dynamically? • Which transcripts are active? • Which proteins are active? • Which proteins interact? Gene Regulation Proteomic profiling Transcript profiling CSE182

5. Counting transcripts • cDNA from the cell hybridizes to complementary DNA fixed on a ‘chip’. • The intensity of the signal is a ‘count’ of the number of copies of the transcript CSE182

6. Quantitation: transcript versus Protein Expression Sample 1 Sample2 Sample 1 Sample 2 Protein 1 35 4 100 20 mRNA1 Protein 2 mRNA1 Protein 3 mRNA1 mRNA1 mRNA1 Our Goal is to construct a matrix as shown for proteins, and RNA, and use it to identify differentially expressed transcripts/proteins CSE182

7. Gene Expression • Measuring expression at transcript level is done by micro-arrays and other tools • Expression at the protein level is being done using mass spectrometry. • Two problems arise: • Data: How to populate the matrices on the previous slide? (‘easy’ for mRNA, difficult for proteins) • Analysis: Is a change in expression significant? (Identical for both mRNA, and proteins). • We will consider the data problem here. The analysis problem will be considered when we discuss micro-arrays. CSE182

8. MS based Quantitation • The intensity of the peak depends upon • Abundance, ionization potential, substrate etc. • We are interested in abundance. • Two peptides with the same abundance can have very different intensities. • Assumption:relative abundance can be measured by comparing the ratio of a peptide in 2 samples. CSE182

9. Quantitation issues • The two samples might be from a complex mixture. How do we identify identical peptides in two samples? • In micro-array this is possible because the cDNA is spotted in a precise location? Can we have a ‘location’ for proteins/peptides CSE182

10. LC-MS based separation HPLC ESI TOF Spectrum (scan) p1 p2 • As the peptides elute (separated by physiochemical properties), spectra is acquired. p3 p4 pn CSE182

11. LC-MS Maps Peptide 2 I Peptide 1 m/z time Peptide 2 elution • A peptide/feature can be labeled with the triple (M,T,I): • monoisotopic M/Z, centroid retention time, and intensity • An LC-MS map is a collection of features x x x x x x x x x x x x x x x x x x x x m/z time CSE182

12. Time scaling: Approach 1 (geometric matching) • Match features based on M/Z, and (loose) time matching. Objective f (t1-t2)2 • Let t2’ = a t2 + b. Select a,b so as to minimize f (t1-t’2)2 CSE182

13. Geometric matching • Make a graph. Peptide a in LCMS1 is linked to all peptides with identical m/z. • Each edge has score proportional to t1/t2 • Compute a maximum weight matching. • The ratio of times of the matched pairs gives a. • Rescale and compute the scaling factor M/Z T CSE182

14. Approach 2: Scan alignment S11 S12 • Each time scan is a vector of intensities. • Two scans in different runs can be scored for similarity (using a dot product) S1i= 10 5 0 0 7 0 0 2 9 S2j= 9 4 2 3 7 0 6 8 3 M(S1i,S2j) = kS1i(k) S2j (k) S21 S22 CSE182

15. Scan Alignment S11 S12 • Compute an alignment of the two runs • Let W(i,j) be the best scoring alignment of the first i scans in run 1, and first j scans in run 2 • Advantage: does not rely on feature detection. • Disadvantage: Might not handle affine shifts in time scaling, but is better for local shifts S21 S22 CSE182

16. MS quantitation Summary • A peptide elutes over a mass range (isotopic peaks), and a time range. • A ‘feature’ defines all of the peaks corresponding to a single peptide. • Matching features is the critical step to comparing relative intensities of the same peptide in different samples. • The matching can be done chemically (isotope tagging), or computationally (LCMS map comparison) CSE182

17. Micro-array analysis CSE182

18. The Biological Problem • Two conditions that need to be differentiated, (Have different treatments). • EX: ALL (Acute Lymphocytic Leukemia) & AML (Acute Myelogenous Leukima) • Possibly, the set of expressed genes is different in the two conditions CSE182

19. Supplementary fig. 2. Expression levels of predictive genes in independent dataset. The expression levels of the 50 genes most highly correlated with the ALL-AML distinction in the initial dataset were determined in the independent dataset. Each row corresponds to a gene, with the columns corresponding to expression levels in different samples. The expression level of each gene in the independent dataset is shown relative to the mean of expression levels for that gene in the initial dataset. Expression levels greater than the mean are shaded in red, and those below the mean are shaded in blue. The scale indicates standard deviations above or below the mean. The top panel shows genes highly expressed in ALL, the bottom panel shows genes more highly expressed in AML. CSE182

20. Gene Expression Data • Gene Expression data: • Each row corresponds to a gene • Each column corresponds to an expression value • Can we separate the experiments into two or more classes? • Given a training set of two classes, can we build a classifier that places a new experiment in one of the two classes. s1 s2 s g CSE182

21. Three types of analysis problems • Cluster analysis/unsupervised learning • Classification into known classes (Supervised) • Identification of “marker” genes that characterize different tumor classes CSE182

22. Supervised Classification: Basics 1 1 2 3 4 5 6 2 g1 3 1 .9 .8 .1 .2 .1 g2 .1 0 .2 .8 .7 .9 • Consider genes g1 and g2 • g1 is up-regulated in class A, and down-regulated in class B. • g2 is up-regulated in class A, and down-regulated in class B. • Intuitively, g1 and g2 are effective in classifying the two samples. The samples are linearly separable. CSE182

23. Basics • With 3 genes, a plane is used to separate (linearly separable samples). In higher dimensions, a hyperplane is used. CSE182

24. Non-linear separability • Sometimes, the data is not linearly separable, but can be separated by some other function • In general, the linearly separable problem is computationally easier. CSE182

25. Formalizing of the classification problem for micro-arrays • Each experiment (sample) is a vector of expression values. • By default, all vectors v are column vectors. • vT is the transpose of a vector • The genes are the dimension of a vector. • Classification problem: Find a surface that will separate the classes v vT CSE182

26. Formalizing Classification • Classification problem: Find a surface (hyperplane) that will separate the classes • Given a new sample point, its class is then determined by which side of the surface it lies on. • How do we find the hyperplane? How do we find the side that a point lies on? 1 2 3 4 5 6 1 2 g1 3 1 .9 .8 .1 .2 .1 g2 .1 0 .2 .8 .7 .9 CSE182

27. Basic geometry • What is ||x||2 ? • What is x/||x|| • Dot product? x=(x1,x2) y CSE182

28. Dot Product • Let  be a unit vector. • |||| = 1 • Recall that • Tx = ||x|| cos  • What is Tx if x is orthogonal (perpendicular) to ? x   Tx = ||x|| cos  CSE182

29. Hyperplane • Find the unit vector that is perpendicular (normal to the hyperplane) • How can we define a hyperplane L? CSE182

30. Points on the hyperplane • Consider a hyperplane L defined by unit vector , and distance 0 • Notes; • For all x  L, xTmust be the same, xT = 0 • For any two points x1, x2, • (x1- x2)T =0 x2 x1 CSE182

31. Hyperplane properties • Given an arbitrary point x, what is the distance from x to the plane L? • D(x,L) = (Tx -0) • When are points x1 and x2 on different sides of the hyperplane? x 0 CSE182

32. Separating by a hyperplane + x2 - x1 • Input: A training set of +ve & -ve examples • Goal: Find a hyperplane that separates the two classes. • Classification: A new point x is +ve if it lies on the +ve side of the hyperplane, -ve otherwise. • The hyperplane is represented by the line • {x:-0+1x1+2x2=0} CSE182

33. Error in classification +  x2 - x1 • An arbitrarily chosen hyperplane might not separate the test. We need to minimize a mis-classification error • Error: sum of distances of the misclassified points. • Let yi=-1 for +ve example i, • yi=1 otherwise. • Other definitions are also possible. CSE182

34. Gradient Descent • The function D() defines the error. • We follow an iterative refinement. In each step, refine  so the error is reduced. • Gradient descent is an approach to such iterative refinement. D() D’()  CSE182

35. Rosenblatt’s perceptron learning algorithm CSE182

36. Classification based on perceptron learning • Use Rosenblatt’s algorithm to compute the hyperplane L=(,0). • Assign x to class 1 if f(x) >= 0, and to class 2 otherwise. CSE182

37. Perceptron learning • If many solutions are possible, it does no choose between solutions • If data is not linearly separable, it does not terminate, and it is hard to detect. • Time of convergence is not well understood CSE182

38. Linear Discriminant analysis • Provides an alternative approach to classification with a linear function. • Project all points, including the means, onto vector . • We want to choose  such that • Difference of projected means is large. • Variance within group is small +  x2 - x1 CSE182

39. LDA Cont’d Fisher Criterion CSE182

40. Maximum Likelihood discrimination • Suppose we knew the distribution of points in each class. • We can compute Pr(x|i) for all classes i, and take the maximum CSE182

41. ML discrimination • Suppose all the points were in 1 dimension, and all classes were normally distributed. CSE182

42. ML discrimination recipe • We know the distribution for each class, but not the parameters • Estimate the mean and variance for each class. • For a new point x, compute the discrimination function gi(x) for each class i. • Choose argmaxi gi(x) as the class for x CSE182